Patent Publication Number: US-2015087125-A1

Title: Method of manufacturing semiconductor device

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority from Japanese Patent Application No. 2013-194769, filed on Sep. 20, 2013, the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a method of manufacturing a semiconductor device. 
     BACKGROUND 
     SiC (silicon carbide) is expected to be a material for next-generation power semiconductor devices. SiC has excellent physical properties, having a band gap three times wider than that of Si (silicon), a breakdown field strength approximately 10 times higher than that of Si, and a heat conductivity approximately three times higher than that of Si. A power semiconductor device that has low loss and is capable of high-temperature operation can be realized by taking advantage of those properties. 
     Meanwhile, it is known that dislocations such as threading screw dislocations (TSDs) or basal plane dislocations (BPDs) in SIC single crystals degrade device characteristics. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic cross-sectional view of a semiconductor device of a first embodiment; 
         FIG. 2  is a flowchart showing a method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 3  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 4  is a schematic cross-sectional view of the liquid phase growth apparatus used by the manufacturing method according to the first embodiment; 
         FIG. 5  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 6  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 7  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 8  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 9  is a diagram for explaining the function of the method of manufacturing the semiconductor device of the first embodiment; 
         FIG. 10  is a diagram for explaining the function of co-doping; 
         FIG. 11  is a diagram for explaining the function of co-doping; 
         FIG. 12  is a diagram for explaining the function of co-doping; 
         FIG. 13  is a diagram for explaining the function of co-doping; 
         FIG. 14  is a diagram for explaining the function of co-doping; 
         FIG. 15  is a diagram showing the relationship between Al and N densities and sheet resistance in the case of n-type SiC; 
         FIG. 16  is a diagram showing the relationship between N and Al densities and sheet resistance in the case of p-type SiC; 
         FIG. 17  is a schematic cross-sectional view of a semiconductor device of a second embodiment; 
         FIG. 18  is a flowchart showing a method of manufacturing the semiconductor device of the second embodiment; 
         FIG. 19  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the second embodiment; 
         FIG. 20  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the second embodiment; 
         FIG. 21  is a schematic cross-sectional view of a semiconductor device of a third embodiment; 
         FIG. 22  is a flowchart showing a method of manufacturing the semiconductor device of the third embodiment; 
         FIG. 23  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the third embodiment; 
         FIG. 24  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the third embodiment; 
         FIG. 25  is a schematic cross-sectional view of a semiconductor device of a fourth embodiment; 
         FIG. 26  is a flowchart showing a method of manufacturing the semiconductor device of the fourth embodiment; 
         FIG. 27  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the fourth embodiment; 
         FIG. 28  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the fourth embodiment; 
         FIG. 29  is a schematic cross-sectional view of a semiconductor device of a fifth embodiment; 
         FIG. 30  is a flowchart showing a method of manufacturing the semiconductor device of the fifth embodiment; and 
         FIG. 31  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of the fifth embodiment. 
     
    
    
     DETAILED DESCRIPTION 
     A method of manufacturing a semiconductor device of an embodiment includes: preparing a substrate; and growing a p-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a p-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element D to the concentration of the element A in the first combination or in the second combination being higher than 0.33 but lower than 1.0. 
     The following is a description of embodiments, with reference to the accompanying drawings. In the following description, like components are denoted by like reference numerals, and explanation of components described once will not be repeated. 
     In the following description, n + , n, n − , p, and p −  indicate relative levels of impurity densities in the respective conductivity types. Specifically, the concentration of an n + -type impurity is relatively higher than the concentration of the corresponding n-type impurity, and the concentration of an n − -type impurity is relatively lower than the concentration of the corresponding n-type impurity. Likewise, the concentration of a p + -type impurity is relatively higher than the concentration of the corresponding p-type impurity, and the concentration of a p − -type impurity is relatively lower than the concentration of the corresponding p-type impurity. It should be noted that there are cases where an n +  type and an n −  type are referred to simply as an n-type, and a p +  type and a p −  type are referred to simply as a p-type. 
     First Embodiment 
     A method of manufacturing a semiconductor device of this embodiment includes: preparing a substrate; and growing a p-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a p-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element D to the concentration of the element A in the first or second combination being higher than 0.33 but lower than 1.0, the concentration of the element A in the combination being not lower than 1×10 16  cm −3  and not higher than 1×10 22  cm −3 . 
     More particularly, an n-type SiC layer is formed on the surface of the SiC single-crystal layer through epitaxial growth, a p-type first SiC region is formed in the surface of the SiC layer, an n-type second SiC region is formed in the surface of the first SiC region, a p-type third SiC region is formed in the surface of the first SiC region, a gate insulating film is formed on the surfaces of the SiC layer and the first SiC region, a gate electrode is formed on the gate insulating film, a first electrode connected to the second SiC region and the third SiC region is formed, and a second electrode connected to the SiC single-crystal layer is formed. 
       FIG. 1  is a schematic cross-sectional view of the structure of an IGBT (Insulated Gate Bipolar Transistor) that is manufactured by a method of manufacturing a semiconductor device of this embodiment. 
     This IGBT  100  includes a p-type SiC single-crystal substrate  10 . This p-type SiC single-crystal substrate  10  is a 4H-SiC substrate (a p-SiC single-crystal substrate) that contains Al (aluminum), for example, as the p-type impurity at an impurity concentration that is not lower than approximately 1×10 18  cm −3  and not higher than approximately 1×10 22  cm −3 . 
     A p-type SiC single-crystal layer (a p-SiC single-crystal layer)  12  formed by a liquid phase growth technique is provided on the p-type SiC single-crystal substrate  10 . The p-type SiC single-crystal layer  12  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element A and the element D form a first combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus). The ratio of the concentration of the element D to the concentration of the element A in the first or second combination (concentration D/concentration A) is higher than 0.33 but lower than 1.0. In this embodiment, the concentration of the element A forming part of the above combination is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 . 
     In the case of the first combination of Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), or In (indium) and N (nitrogen), for example, the element A may be a single element selected from Al (aluminum), Ga (gallium), and in (indium). Alternatively, the element A may be formed with two elements such as Al (an element A 1 ) and Ga (an element A 2 ) or may be formed with three elements such as Al (the element A 1 ), Ga (the element A 2 ), and In (an element A 3 ). In a case where the element A is formed with more than one element, the element A may be formed with two or three kinds of elements, as long as the above described conditions on the ratio of the concentration of the element D to the concentration of the element A and on the concentration of the element A are satisfied. 
     The first combination and the second combination can coexist. However, the above described conditions on the ratio of the concentration of the element D to the concentration of the element A and on the concentration of the element A should be satisfied with elements that form at least one of the first and second combinations. In other words, each of the first combination and the second combination should satisfy the conditions on the element ratio and the element concentration. This is because the later described trimers are not formed between an impurity in the first combination and an impurity in the second combination. 
     In a case where the Al concentration is 1×10 18  cm −3 , the Ga concentration is 1×10 18  cm −3 , and the N concentration is 1×10 18  cm −3 , for example, N/(Al+Ga) is 0.5, and (Al+Ga is 2×10 18  cm −3 . In this case, the element ratio and the element densities are within the ranges set by this embodiment. 
     In a case where the B concentration is 4×10 18  cm −3 , the P concentration is 1×10 18  cm −3 , and the N concentration is 1×10 18  cm −3 , for example, attention is paid only to B and P, which forms the second combination. As a result, P/B is 0.25, which does not satisfy the element ratio condition, and is outside the range set by this embodiment. 
     Also, in a case where the Al concentration is 5×10 17  cm −3 , the B concentration is 5×10 17  cm −3 , the N concentration is 2.5×10 17  cm −3 , and the P concentration is 2.5×10 17  cm −3 , N/Al is 0.5, which satisfies the ratio condition, but the Al concentration is lower than 1×10 18  cm −3  in the first combination. In the second combination, P/B is 0.5, which satisfies the ratio condition, but the B concentration is lower than 1×10 18  cm −3 . Therefore, either of the first and second combinations does not satisfy the element ratio condition and the element concentration condition, and is outside the ranges set by this embodiment. 
     It should be noted that this embodiment does not exclude elements other than the above mentioned elements as p-type impurities and n-type impurities. In the following, an example case where the element A is Al (aluminum) and the element D is N (nitrogen) is described. 
     The Al concentration in the p-SiC single-crystal layer  12  is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 . The thickness of the p-SiC single-crystal layer  12  is not smaller than 1 μm and not greater than 350 μm, for example. 
     An n-type SiC layer (an n − -SiC layer)  14  containing the n-type impurity at an impurity concentration that is not lower than 5×10 15  cm −3  and not higher than 2×10 16  cm −3 , for example, is formed on the surface of the p-SiC single-crystal layer  12 . The thickness of the n − -SiC layer  14  is not smaller than 5 μm and not greater than 120 μm, for example. 
     A p-type first SiC region (a first emitter region)  66  containing the p-type impurity at an impurity concentration that is not lower than 5×10 15  cm −3  and not higher than 1×10 17  cm −3 , for example, is formed in part of the surface of the n − -SiC layer  14 . The depth of the first emitter region  66  is approximately 0.6 μm, for example. 
     An n + -type second SiC region (a second emitter region)  58  containing the n-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the first SiC region (the first emitter region)  66 . The depth of the second emitter region  58  is smaller than the depth of the first SiC region (the first emitter region)  66 , and is approximately 0.3 μm, for example. 
     A p + -type third SiC region (an emitter contact region)  60  containing the p-type impurity at an impurity concentration, that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the first SiC region (the first emitter region)  66  and on a side of the n + -type second SiC region (the second emitter region)  58 . The depth of the emitter contact region  60  is smaller than the depth of the first SiC region (the first emitter region)  66 , and is approximately 0.3 μm, for example. 
     Agate insulating film  28  is continuously formed on the surfaces of the n − -SiC layer  14  and the first SiC region (the first emitter region)  66 , so as to bridge the space between the layer and the region. The gate insulating film  28  may be a silicon oxide film (a SiO 2  film), a silicon oxynitride film, or a high-k insulating film, for example. 
     A gate electrode  30  is formed on the gate insulating film  28 . The gate electrode  30  may be made of polysilicon, for example. An interlayer insulating film  32  formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     The first SiC region  66  that is located below the gate electrode  30  and is interposed between the second SiC region (the second emitter region)  58  and the n − -SiC layer  14  serves as the channel region. 
     A conductive first electrode (an emitter electrode)  54  that is electrically connected to the second SiC region (the second emitter region)  58  and the third SiC region (the emitter contact region)  60  is provided. The first electrode (the emitter electrode)  54  is formed with a Ni (nickel) barrier metal layer  54   a  and an Al metal layer  54   b  formed on the barrier metal layer  54   a , for example. The Ni barrier metal layer  54   a  and the Al metal layer  54   b  may form an alloy through a reaction. 
     A conductive second electrode (a collector electrode)  56  is formed on the bottom surface of the p-SiC single-crystal substrate  10 . The second electrode (the collector electrode)  56  is made of Ni, for example. 
     Next, a method of manufacturing the semiconductor device of this embodiment is described. 
       FIG. 2  is a flowchart showing an example of the method of manufacturing the semiconductor device of this embodiment.  FIG. 3  and  FIGS. 5 through 8  are schematic cross-sectional views illustrating the method of manufacturing the semiconductor device of this embodiment.  FIG. 4  is a schematic cross-sectional view of the liquid phase growth apparatus used by the manufacturing method according to this embodiment. 
     As shown in  FIG. 2 , the method of manufacturing the semiconductor device includes: p-SiC single-crystal substrate preparation (step S 100 ); p-SiC single-crystal layer formation by a liquid phase growth technique (step S 101 ); n − -SiC layer formation (step S 102 ); p-type impurity ion implantation (step S 104 ); n-type impurity ion implantation (step S 106 ); p-type impurity ion implantation (step S 108 ); annealing (step S 110 ); gate insulating film formation (step S 112 ); gate electrode formation (step S 114 ); interlayer film formation (step S 116 ); first electrode formation (step S 118 ); second electrode formation (step S 120 ); and annealing (step S 122 ). 
     First, in step S 100 , the 4H-SiC p-type SiC single-crystal substrate (the p-SiC single-crystal substrate)  10  that contains Al (aluminum) as the p-type impurity at an impurity concentration of approximately 5×10 18  cm −3 , has low resistance, and has a thickness of 200 μm, for example, is prepared. 
     In step S 101 , the p-type SiC single-crystal layer  12  is formed on the surface of the p-SiC single-crystal substrate  10  through epitaxial growth by a liquid phase growth technique ( FIG. 3 ). The surface of the p-SiC single-crystal substrate  10  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. 
       FIG. 4  is a schematic cross-sectional view of the liquid phase growth apparatus used for forming the p-type SiC single-crystal layer  12 . The liquid phase growth apparatus includes a crucible  2  that stores a liquid phase  1 , a supporting unit  4  that is capable of supporting a seed crystal  3  at its end portion, and a heater  5  that heats the liquid phase  1  and the seed crystal  3 . The crucible  2  is made of graphite, for example. 
     In step S 101 , at the supporting unit  4 , the p-SiC single-crystal substrate  10  is secured as the seed crystal  3  to the end portion of the supporting unit  4 . The liquid phase  1  in the crucible  2  is heated to a temperature that is not lower than 1800° C. and not higher than 2100° C., for example, by the heater  5 . The liquid phase  1  contains Si (silicon), C (carbon), the p-type impurity, and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element A and the element D form a first combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus). The ratio of the concentration of the element D to the concentration of the element A in the first or second combination is higher than 0.33 but lower than 1.0. In this embodiment, the element A is Al, and the element D is N. 
     The surface of the p-SiC single-crystal substrate  10  is immersed in the liquid phase  1 , to form the p-type SiC single-crystal layer (the p-SiC single-crystal layer)  12  on the surface of the p-SiC single-crystal substrate  10  through epitaxial growth from the liquid phase  1 . 
     The formed p-SiC single-crystal layer  12  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element A and the element D form a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus). The ratio of the concentration of the element D to the concentration of the element A in the first or second combination (concentration D/concentration A) is higher than 0.33 but lower than 1.0. In this embodiment, the element A is Al, and the element D is N. 
     The Al concentration in the p-SiC single-crystal layer  12  is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example. The densities of the p-type impurity and the n-type impurity in the p-SiC single-crystal layer  12  can be adjusted to desired values by controlling the densities of the p-type impurity and the n-type impurity in the liquid phase  1 . 
     The thickness of the p-SiC single-crystal layer  12  is not smaller than 1 μm and not greater than 350 μm, for example. 
     In step S 102 , the high-resistance n − -SiC layer  14  that contains N as the n-type impurity at an impurity concentration of approximately 1×10 16  cm −3 , for example, and has a thickness of approximately 100 μm is grown on the surface of the p-SiC single-crystal layer  12  by an epitaxial growth technique. 
     After that, patterning is performed by photolithography and etching, to form a first mask material  42  that is made of SiO 2 , for example. In step S 104 , Al as the p-type impurity is implanted into the n − -SiC layer  14  through ion implantation by using the first mask material  42  as an ion implantation mask, to form the first SiC region (the first emitter region)  66  ( FIG. 5 ). 
     After that, patterning is performed by photolithography and etching, to form a second mask material  44  that is made of SiO 2 , for example. In step S 106 , N as the n-type impurity is implanted into the n − -SiC layer  14  through ion implantation by using the second mask material  44  as an ion implantation mask, to form the n-type second SiC region (the second emitter region)  58  ( FIG. 6 ). 
     After that, patterning is performed by photolithography and etching, to form a third mask material  46  that is made of SiO 2 , for example. In step S 108 , Al as the p-type impurity is implanted into the n − -SiC layer  14  through ion implantation by using the third mask material  46  as an ion implantation mask, to form the p-type third SiC region (the emitter contact region)  60  ( FIG. 7 ). 
     In step S 110 , annealing is performed to activate the p-type impurity and the n-type impurity that have been ion-implanted. The conditions for the annealing are that an argon (Ar) gas is used as the atmosphere gas, the heating temperature is 1600° C., and the heating period is 30 minutes, for example. At this point, the impurities implanted into the SiC can be activated, but diffusion is small. 
     In step S 112 , the gate insulating film  28  that is formed with a SiO 2  film, for example, is formed by CVD (Chemical Vapor Deposition) or thermal oxidation. In step S 114 , the gate electrode  30  that is made of polysilicon, for example, is formed on the gate insulating film  28 . In step S 116 , the interlayer insulating film  32  that is formed with a SiO 2  film, for example, is formed on the gate electrode  30  ( FIG. 8 ). 
     After that, in step S 118 , the conductive first electrode (the emitter electrode)  54  that is electrically connected to the second SiC region (the emitter region)  58  and the third SiC region (the emitter contact region)  60  is formed. The first electrode (the emitter electrode)  54  is formed by Ni (nickel) and Al sputtering, for example. 
     In step S 120 , the conductive second electrode (the collector electrode)  56  is formed on the bottom surface of the p-SiC single-crystal substrate  10 . The second electrode (the collector electrode)  56  is formed by Ni sputtering, for example. 
     In step S 122 , annealing is performed to lower the contact resistance between the first electrode  54  and the second electrode  56 . The annealing is performed in an argon gas atmosphere at 1000° C., for example. 
     By the above described manufacturing method, the IGBT  100  shown in  FIG. 1  is formed. 
       FIG. 9  is a diagram for explaining the effects of the method of manufacturing the semiconductor device of this embodiment. In this embodiment, the p-SiC single-crystal substrate  10  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. 
     In the p-SiC single-crystal substrate  10 , threading screw dislocations (TSDs) exist in a region extending from the inside to the surface. If the p-SiC single-crystal layer  12  and the n − -SiC layer  14  are epitaxially grown by a vapor phase growth technique on the p-SiC single-crystal substrate  10  having TSDs in its surface, the TSDs might extend into the n − -SiC layer  14 , and reach the surface of the n − -SiC layer  14 , as indicated by the dashed line in  FIG. 9 . For example, the gate insulating film  28  is formed by thermal oxidation in the surface of the n − -SiC layer  14  having TSDs in the surface. In that case, the reliability of the gate insulating film  28  becomes lower due to the TSDs. 
     In this embodiment, the p-SiC single-crystal layer  12  is formed on the surface of the p-SiC single-crystal substrate  10  by using a liquid phase growth technique. With the liquid phase growth technique, TSDs are converted into basal plane dislocations (BPDs) in the p-SiC single-crystal layer  12 . BPDs extend along the {0001} plane, and exit the p-SiC single-crystal layer  12  from a side surface. In other words, the BPDs extend in accordance with the off angle, and exit from a side surface. In this manner, the TSDs are restrained from reaching the surface of the n − -SiC layer  14 . Accordingly, the reliability of the gate insulating film  28  formed on the surface of the n − -SiC layer  14  is increased. 
     If BPDs exist in the n − -SiC layer  14 , there is also a possibility that the on-state resistance increases at the time of forward-current application to the IGBT  100 , and device characteristics might be degraded. According to this embodiment, BPDs exit the p-SiC single-crystal layer  12  from a side surface, and the BPDs are restrained from extending into the n − -SiC layer  14 . Accordingly, degradation of device characteristics due to BPDs can also be prevented. 
     The surface of the p-SiC single-crystal substrate  10  preferably has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees, or more preferably, not smaller than 2 degrees and not larger than 6 degrees, with respect to the {0001} plane. If the off angle is below the range, stable epitaxial growth might not be achieved. If the off angle is above the range, the unevenness of the crystal surface becomes larger, and the reliability of the gate insulating film formed on the surface might become lower. If the off angle is above the range, the efficiency at which BPDs converted from TSDs are released from a crystal side surface might become lower. 
     In this embodiment, the p-SiC single-crystal layer  12  is co-doped with Al (aluminum) as the p-type impurity and N (nitrogen) as the n-type impurity at a predetermined ratio. With this arrangement, resistance of the p-SiC single-crystal layer  12  is lowered. Accordingly, on-state resistance of the IGBT  100  is lowered. 
     In this embodiment, the n-type impurity is preferably N (nitrogen) or P (phosphorus), for example, but it is possible to use As (arsenic) or the like. Also, the p-type impurity is preferably Al (aluminum), for example, but it is possible to use B (boron), Ga (gallium), In (indium), or the like. 
     In the following, the function and effects of the co-doping of this embodiment are described in detail. 
     It has become apparent from the results of studies made by the inventors that pairing between Al and N can be caused by co-doping SiC with Al as the p-type impurity (p-type dopant) and N as the n-type impurity (n-type dopant). In this pairing state, carrier compensation occurs, and a zero-carrier state is formed. 
       FIGS. 10 and 11  are diagrams for explaining the function of co-doping.  FIG. 10  shows the case of n-type SiC, and  FIG. 11  shows the case of p-type SiC. It has become apparent from the first principle calculation performed by the inventors that Al enters Si (silicon) sites and N enters C (carbon) sites in SiC so that Al and N become adjacent to each other, and, as a result, the system becomes stable. 
     Specifically, as shown in  FIGS. 10 and 11 , where Al and N are linked to each other to form Al—N pair structures, the system becomes 2.9 eV more stable in terms of energy than a system in which Al and N are not linked to each other but exist independently of each other. If the Al amount and the N amount are the same, the most stable state is achieved when all of the two elements form pair structures. 
     Here, the first principle calculation is a calculation using ultrasoft pseudopotential. Ultrasoft pseudopotential is a type of pseudopotential, and was developed by Vanderbilt et al. For example, a lattice constant has such a high precision as to realize experimental values with a margin of error of 1% or less. Structural relaxation is achieved by introducing impurities (dopant), and the entire energy of a stable state is calculated. The energy of the entire system after a change is compared with the energy prior to the change, so as to determine which structures are in a stable state. In a stable state, in which energy positions impurity levels are located in the band gap can be indicated. 
     As shown in  FIG. 10 , it has become apparent that, in a case where the amount of N is larger than the amount of Al, or in the case of n-type SiC, extra N enters C sites located in the vicinities of Al—N pair structures, to form N—Al—N trimers and further stabilize the system. According to the first principle calculation, trimers are formed, and the system becomes 0.3 eV more stable than a system in which pair structures exist separately from N. 
     Likewise, as shown in  FIG. 11 , it has become apparent that, in a case where the amount of Al is larger than the amount of N, or in the case of p-type SiC, extra Al enters Si sites located in the vicinities of Al—N pair structures, to form Al—N—Al trimers and further stabilize the system. According to the first principle calculation, trimers are formed, and the system becomes 0.4 eV more stable than a system in which Al—N pair structures exist separately from Al. 
     Next, dopant combinations other than the combination of Al and N are discussed. Calculation results obtained in a case where a calculation was conducted for a combination of B (boron) and N (nitrogen) are described below. 
     B enters Si sites, and N enters C sites. According to the first principle calculation, B—N—B or N—B—N trimeric structures cannot be formed. Specifically, B—N pair structures are formed, but the energy of the system becomes higher when B or N approaches the B—N pair structures. Accordingly, the system is more stable in terms of energy when extra B or N exists in positions sufficiently away from the pair structures. 
     According to the first principle calculation, when extra B forms trimers, the energy of the system is 0.5 eV higher than that in a case where B-N pairs exist independently of B. Also, when extra N forms trimers, the energy of the system is 0.3 eV higher than that in a case where B-N pairs exist independently of N. Therefore, in either case, the system becomes unstable in terms of energy when trimers are formed. 
       FIG. 12  is a diagram for explaining the function of co-doping.  FIG. 12  shows the covalent radii of respective elements. Elements with smaller covalent radii are shown in the upper right portion in the drawing, and elements with larger covalent radii are shown in the lower left portion. 
     Considering the covalent radii, it is understandable that the system becomes unstable when trimers are formed with B and N. The covalent radius of B is smaller than the covalent radius of Si, and the covalent radius of N is smaller than the covalent radius of C. Therefore, when B enters Si sites and N enters C sites, strain accumulates, and trimers cannot be formed. 
     It has become apparent that trimers are not formed with combinations of the p-type impurity and the n-type impurity as dopant other than the combinations of “an element (Al, Ga, or In) having a larger covalent radius than Si” and “an element (N) having a smaller covalent radius than C”, and the reverse combination of “an element (B) having a larger covalent radius than C” and “an element (P) having a smaller covalent radius than Si”. 
     Since the covalent radii of B and P are between the covalent radius of Si and the covalent radius of C, B and P can enter both Si sites and C sites. However, the other impurities (Al, Ga, In, N, and As) basically enter either Si sites or C sites. It is safe to say that Al, Ga, In, and As enter Si sites, and N enters C sites. 
     Furthermore, when both impurities enter Si sites or both impurities enter C sites, there is no need to take into account such an aspect. This is because it is difficult to relax strain unless the p-type impurity and the n-type impurity are located at the closest distance from each other. Therefore, where the p-type impurity is the element A and the n-type impurity is the element D, it is difficult to form trimers with combinations of the element A and the element D other than the four combinations of “Al and N”, “Ga and N”, “In and N”, and “B and P”. 
     The pair structures or the trimeric structures cannot be formed unless there is interaction between atoms. If approximately 10 unit cells exist in the c-axis direction, the interaction is invisible, and the impurity levels (dopant levels) in a 4H-SiC structure according to the first principle calculation are in a flat state. That is, diffusion is sufficiently restrained, and is on the order of approximately 10 meV. 
     In other words, it is considered that there is little interaction when the distance between impurities is 10 nm or longer. In view of this, to maintain interaction between impurities, the impurity densities are preferably 1×10 18  cm −3  or higher. 
     This value is the lower limit of impurity densities that is desired when a local impurity distribution is formed through ion implantation in a case where a SiC material has already been formed. With a liquid phase growth technique or a vapor phase growth technique, the lower limit of impurity densities becomes even lower. 
     To cause an effect of co-doping to appear in semiconductor SiC, the ratio between the n-type impurity concentration and the p-type impurity concentration needs to be restricted within a specific range. By the later described manufacturing method, it is critical that the ratio between the n-type and p-type impurities to be introduced by ion implantation be set at a ratio within the specific range from the start. Although the reach of interaction is as short as less than 10 nm, trimers can be formed by virtue of the attraction force of each other within the reach. Furthermore, as the attraction force is applied, the temperature of the activating anneal for the impurities can be lowered from 1700-1900° C., which is the temperature range in a case where co-doping is not performed, to 1500-1800° C. 
     However, the impurity concentration desirable for trimer formation can be lowered in crystal growth from a vapor phase by CVD (Chemical Vapor Deposition) or the like. This is because precursor gases can be made to flow in the surface, and accordingly, interaction between the impurities can easily occur at low densities. 
     When trimers are to be formed at the time of crystal growth from a vapor phase, the densities of the p-type and n-type impurities are preferably 1×10 15  cm −3  or higher. Further, so as to facilitate the trimer formation, the impurity densities are preferably 1×10 16  cm −3  or higher. 
     When trimers are formed, the upper limit of impurity densities may exceed the solid solubility limit of cases where trimers are not formed. This is because, when trimers are formed, strain in crystals is relaxed, and the impurities are easily incorporated. 
     The impurity solid solubility limit in a case where trimers are not formed is on the order of 10 19  cm −3  in the case of N, and is on the order of 10 21  cm −3  even in the case of Al. As for the other impurities, the solid solubility limit is on the order of approximately 10 21  cm −3 . 
     When only one type of impurity is used, the size of the impurity is either small or large. Therefore, strain accumulates, and the impurity cannot easily enter lattice points. As a result, activation cannot be caused. Particularly, in the case of ion implantation, a large number of defects are formed, and the solid solubility limit becomes even lower. 
     However, when trimers are formed, both Al and N can be implanted up to the order of approximately 10 22  cm −3 . As strain can be relaxed by forming trimers with one of the four combinations of “Al and N”, “Ga and N”, “In and N”, and “13 and P”, the solid solubility limit can be extended. As a result, the impurity solid solubility limit can be extended to the order of 10 22  cm −3 . 
     In a case where the impurity is B, Al, Ga, In, or P, strain is large, and a large number of defects exist, if the impurity concentration is 1×10 20  cm −3  or higher, or more particularly, 6×10 20  cm −3  or higher. As a result, sheet resistance or resistivity becomes very high. 
     However, co-doping with the p-type impurity and the n-type impurity can reduce defects even in regions having such high impurity densities. 
     When an impurity is N, the solid solubility limit is further lowered by one digit to approximately 2×10 19  cm −3 . According to the first principle calculation, this is probably because defects of inactive interstitial N are formed. 
     As trimers are formed, the upper limit of the N concentration is dramatically increased from the order of 10 19  cm −3  to the order of 10 22  cm −3 . In a case where an n-type region doped at a high concentration is to be formed, nitrogen cannot be normally used, and P ions are implanted at approximately 10 20  cm −3 , for example. In this embodiment, however, an n-type region doped at a high concentration can be formed by using nitrogen. For example, N is implanted at 2×10 20  cm −3 , and Al is implanted at 1×10 20  cm −3 . It is normally difficult to use nitrogen, but nitrogen can be used in this embodiment. 
     As described above, both the p-type impurity and the n-type impurity are implanted, and an appropriate combination of covalent radii is selected, so that trimers can be formed. The structures are then stabilized, and strain can be reduced. 
     As a result, (1) the respective impurities can easily enter lattice points, (2) the process temperature can be lowered, and a temperature decrease of at least 100° C. can be expected, (3) the amount of impurities that can be activated increases (the upper limit is extended), (4) stable structures such as trimers or pair structures can be formed, and entropy is increased and crystal defects are reduced with the structures, and (5) as the trimers are stable, revolutions around the bonds that bind the p-type impurity and the n-type impurity become difficult, and the structures are immobilized. Accordingly, energization breakdown tolerance becomes dramatically higher. For example, when trimeric structures are formed in at least part of the p-type impurity region and the n-type impurity region of a pn junction, energization breakdown is restrained, and an increase in resistance can be avoided. As a result, a degradation phenomenon (Vf degradation) in which the voltage (Vf) required to be applied so as to apply a certain amount of current becomes higher can be restrained. 
     As described above, pairing between Al and N can be caused by co-doping with Al as the p-type impurity and N as the n-type impurity. Furthermore, it has become apparent from the first principle calculation that both acceptor levels and donor levels can be made shallower at this point. 
       FIGS. 13 and 14  are diagrams for explaining the function of co-doping.  FIG. 13  shows the case of n-type SiC, and  FIG. 14  shows the case of p-type SiC. White circles represent empty levels not filled with electrons, and black circles represent levels filled with electrons. 
     The reason that the donor levels become shallower is that the empty levels located within the conduction band of Al as the acceptor interact with the donor levels of N, and the donor levels are raised, as shown in  FIG. 13 . Likewise, the reason that the acceptor levels become shallower is that the levels that are filled with electrons and are located within the valence band of N as the donor interact with the acceptor levels of Al, and the acceptor levels are lowered, as shown in  FIG. 14 . 
     Normally, N or P (phosphorus) as the n-type impurity forms donor levels that are as deep as 42 to 95 meV. B, Al, Ga, or In as the p-type impurity forms very deep acceptor levels of 160 to 300 meV. If trimers are formed, on the other hand, the n-type impurity can form donor levels of 35 meV or lower, and the p-type impurity can form acceptor levels of 100 meV or shallower. 
     In an optimum state where trimers are completely formed, n-type N or P forms levels of approximately 20 meV, and p-type B, Al, Ga, or In forms levels of approximately 40 meV. As such shallow levels are formed, most of the activated impurities turn into carriers (free electrons and free holes). Accordingly, the bulk resistance becomes one or more digits lower than that in a case where co-doping is not performed. 
     In the case of n-type SiC, the donor levels that contribute to carrier generation becomes 40 meV or shallower, and as a result, the resistance becomes lower than that in a case where co-doping is not performed. Also, as the donor levels become 35 meV or shallower, the resistance is lowered by approximately one digit. As the donor levels become 20 meV or shallower, the resistance is lowered by approximately two digits. However, a strain relaxation effect and a doping upper limit extension effect are also achieved. 
     In the case of p-type SiC, the acceptor levels that contribute to carrier generation become 150 meV or shallower, and as a result, the resistance becomes lower than that in a case where co-doping is not performed. Also, as the acceptor levels become 100 meV or shallower, the resistance is lowered by approximately one digit. As the acceptor levels become 40 meV or shallower, the resistance is lowered by approximately two digits. However, a strain relaxation effect and a doping upper limit extension effect are also achieved. 
     When the Al concentration and the N concentration are the same (N:Al=1:1), an insulator is formed, because there are no carriers though there are shallow levels. There exist carriers that are equivalent to a difference between the Al concentration and the N concentration. To form a low-resistance semiconductor, a concentration difference is required. 
     When the N concentration is higher than the Al concentration (N concentration&gt;Al concentration), extra N generated as a result of formation of Al—N pairs through interaction is also stabilized by substituting C located in the vicinities of the Al—N pairs. Accordingly, shallow donor levels are formed. Also, strain is relaxed. Accordingly, the N concentration can be made higher than that in a case where trimers are not formed. 
       FIG. 15  is a diagram showing the relationship between Al and N densities and sheet resistance in the case of n-type SiC. The N concentration is 2×10 20  cm −3 . When only N is implanted, the sheet resistance cannot be lowered even if N is implanted at 1×10 19  cm −3  or higher. The value is approximately 300Ω/□. 
     While “N concentration:Al concentration” is changing from 1:1 to 2:1, trimers are formed without strain, and the number of carrier electrons in the shallow donor levels increases. Accordingly, the sheet resistance rapidly decreases. 
     When the ratio reaches 2:1, the maximum amount of carriers is available, and the sheet resistance becomes lowest. As shown in  FIG. 15 , the sheet resistance can be lowered down to approximately 1.5Ω/□. The contact resistance to n-type SiC can also be lowered from approximately 10 − Ωcm 3  to approximately 10 −7  Ωcm 3  by making “N concentration:Al concentration” equal to 2:1 and increasing the difference between the N concentration and the Al concentration from 10 20  cm −3  to 10 22  cm −3 . 
     Furthermore, if the ratio of the N concentration becomes higher than 2:1, the original deep donor levels are formed by the extra N that exceeds “N concentration:Al concentration=2:1”. The donor levels receive carrier electrons, and the shallow donor levels formed with trimers become empty. The excess N left out from “N concentration:Al concentration=2:1” is similar to N introduced independently. Therefore, strain relaxation is difficult. As a result, the sheet resistance rapidly increases as shown in  FIG. 15 . 
     In  FIG. 15 , the target for comparison is the sheet resistance (approximately 300Ω/□ in this case) in a case where N (nitrogen) as the n-type impurity is implanted almost up to the solid solubility limit when co-doping with Al is not performed, and changes in the sheet resistance value seen when “N concentration:Al concentration” is changed from 2:1 are shown. 
     The following description centers around “Al concentration/N concentration=0.5”, at which trimer structures are formed. In a case where “Al concentration/N concentration” is not lower than 0.47 and not higher than 0.60 (100% of the carriers of 8×10 19  cm −3  or higher being free carriers), or where the p-type impurity is implanted at 47 to 6.0% with respect to the n-type impurity, the sheet resistance is two digits lower than the sheet resistance obtained in a case where co-doping with Al is not performed. Such a concentration ratio is highly advantageous. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 8×10 19  cm −3  are obtained when the ratio is approximately 0.47 
     In a case where the range is widened in both directions, and “Al concentration/N concentration” is not lower than 0.45 and not higher than 0.75 (100% of the carriers of 5×10 19  cm −3  or higher being free carriers), or where Al is implanted at 45 to 75% with respect to N, the sheet resistance ranges from a two-digit-lower resistance to a resistance almost three times higher than the two-digit-lower resistance. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 5×10 19  cm −3  are obtained when the ratio is approximately 0.45. In a case where the range is further widened in both directions and “Al concentration/N concentration” is higher than 0.40 but lower than 0.95 (100% of the carriers of 1×10 19  cm −3  or higher being free carriers), or where Al is implanted at 40 to 95% with respect to N, the sheet resistance becomes one digit lower. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 1×10 19  cm −3  are obtained when the ratio is approximately 0.40. 
     Better characteristics are achieved on the side where Al is implanted at 50% or more with respect to N, because strain is sufficiently relaxed. The 50% state is the state where two N atoms and one Al atom are clustered to form a trimer. When the ratio is lower than 50%, trimers are formed, and extra N exists. Since there is N that cannot form trimers, an equivalent amount of strain accumulates. N that cannot form trimers is the same as that introduced independently, and reaches the limit of strain in no time. When the amount of Al is lower than 50%, strain rapidly occurs, and lattice defects increase. Therefore, the sheet resistance rapidly deteriorates when the ratio is lower than 50%, compared with that in a case where the ratio is 50% or higher at which strain can be relaxed. 
     When “Al concentration/N concentration” is 0.995, the number of carriers is almost the same as that in a case where co-doping is not performed. Since 100% of the carriers of 1×10 18  cm −3  or higher, which is 0.5% of 2×10 20  cm −3 , are free carriers, the sheet resistance to be obtained with conventional nitrogen doping can be realized. Accordingly, the sheet resistance is almost the same as that in a case where co-doping is not performed. In a case where “Al concentration/N concentration” is 0.33 or where “N concentration:Al concentration” is 3:1, all carrier electrons are received not by shallow donor levels formed with trimers but by deep donor levels formed with extra N. Accordingly, the sheet resistance is almost the same as that in a case where co-doping is not performed. Therefore, the resistance is lowered by co-doping in cases where “Al concentration/N concentration” is higher than 0.33 but lower than 0.995, or where Al is implanted at 33 to 99.5% with respect to N. With the margin of error being taken into account, it can be considered that the ratio of Al to N should be higher than 33% but lower than 100%. 
     When the Al concentration is higher than the N concentration (Al concentration&gt;N concentration), extra Al generated as a result of formation of Al—N pairs through interaction is also stabilized by substituting Si located in the vicinities of the Al—N pairs. Accordingly, shallow acceptor levels are formed. Also, strain is relaxed. Accordingly, the Al concentration can be made higher than that in a case where trimers are not formed. This case can be considered to be the same as the case where the N concentration is higher than the Al concentration. 
       FIG. 16  is a diagram showing the relationship between N and Al densities and sheet resistance in the case of p-type SiC. The Al concentration is 2×10 20  cm −3 . 
     While “Al concentration:N concentration” is changing from 1:1 to 2:1, trimers are formed without strain, and the number of carrier holes in the shallow acceptor levels increases. Accordingly, the sheet resistance decreases. 
     When the ratio reaches 2:1, the maximum amount of carriers is available, and the sheet resistance becomes lowest. As shown in  FIG. 16 , the sheet resistance can be lowered down to approximately 40Ω/□. The contact resistance to p-type SiC can also be lowered from approximately 10 −5  Ωcm 3  to approximately 10 −7  Ωcm 3  by making “Al concentration:N concentration” equal to 2:1 and increasing the difference between the Al concentration and the N concentration from 10 20  cm −3  to 10 −3 . 
     Furthermore, if the ratio of the Al concentration becomes higher than 2:1, the original deep acceptor levels are formed by the extra Al that exceeds “Al concentration:N concentration=2:1”. The acceptor levels receive carrier holes, and the shallow acceptor levels formed with trimers are filled with electrons. The excess Al left out from “Al concentration:N concentration=2:1” is similar to N introduced independently. Therefore, strain relaxation is difficult. As a result, the sheet resistance rapidly increases as shown in  FIG. 16 . 
     In  FIG. 16 , the target for comparison is the sheet resistance (approximately 10 KΩ/□ in this case) in a case where Al (aluminum) as the p-type impurity is implanted almost up to the solid solubility limit when co-doping with N is not performed, and changes in the sheet resistance value seen when “Al concentration:N concentration” is changed from 2:1 are shown. 
     The following description centers around “N concentration/Al concentration=0.5”, at which trimer structures are formed. In a case where “N concentration/Al concentration” is not lower than 0.47 and not higher than 0.60 (100% of the carriers of 8×10 19  cm −3  or higher being free carriers), or where the n-type impurity is implanted at 47 to 60% with respect to the p-type impurity, the sheet resistance is two digits lower than the sheet resistance obtained in a case where co-doping with N is not performed. Such a concentration ratio is highly advantageous. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 8×10 19  cm −3  are obtained when the ratio is approximately 0.47 
     In a case where the range is widened in both directions, and “N concentration/Al concentration” is not lower than 0.45 and not higher than 0.75 (100% of the carriers of 5×10 19  cm −3  or higher being free carriers), or where N is implanted at 45 to 75% with respect to Al, the sheet resistance ranges from a two-digit-lower resistance to a resistance almost three times higher than the two-digit-lower resistance. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 5×10 19  cm −3  are obtained when the ratio is approximately 0.45. In a case where the range is further widened in both directions and “N concentration/Al concentration” is higher than 0.40 but lower than 0.95 (100% of the carriers of 1×10 19  cm −3  or higher being free carriers), or where N is implanted at 40 to 95% with respect to Al, the sheet resistance becomes one digit lower. When the ratio is lower than 0.5, shallow levels decrease, and strain is caused. As a result, the number of free carriers decreases, and carriers equivalent to 1×10 19  cm −3  are obtained when the ratio is approximately 0.40. 
     Better characteristics are achieved in cases where N is implanted at 50% or more with respect to Al, because strain is relaxed. When N is less than 50%, on the other hand, trimers formed with one N atom and two Al atoms that are clustered account for 50% of the entire structure, and further, Al exists therein. Since there is Al that cannot form trimers, an equivalent amount of strain accumulates. When the amount of N is lower than 50%, strain rapidly occurs, and lattice defects increase. Therefore, the sheet resistance rapidly deteriorates when the ratio is lower than 50%, compared with that in a case where the ratio is 50% or higher at which strain can be relaxed. 
     At this point, “N concentration/Al concentration” is 0.995, and the number of carriers is almost the same as that in a case where co-doping is not performed. Since 100% of the carriers of 1×10 18  cm −3  or higher, which is 0.5% of 2×10 20  cm −3 , are free carriers, the sheet resistance to be achieved with conventional Al doping can be realized. Accordingly, the sheet resistance is almost the same as that in a case where co-doping is not performed. In a case where “N concentration/Al concentration” is 0.33 or where “Al concentration:N concentration” is 3:1, all carrier holes are received not by shallow acceptor levels formed with trimers but by deep acceptor levels formed with extra Al. Accordingly, the sheet resistance is almost the same as that in a case where co-doping is not performed. Therefore, a resistance lowering effect is achieved by co-doping in cases where “N concentration/Al concentration” is higher than 0.33 but lower than 0.995, or where N is implanted at 33 to 99.5% with respect to Al. With the margin of error being taken into account, it can be considered that the ratio of Al to N should be higher than 33% but lower than 100%. 
     When co-doping is not performed, a low-resistance SiC semiconductor material containing impurities having low densities of 1×10 18  cm −3  or lower cannot exist. However, when trimers are formed by co-doping, shallow levels are formed, and the number of carriers increases. Accordingly, a reduction in resistance can be achieved with small amounts of impurities. 
     Co-doping with the p-type impurity and the n-type impurity at an appropriate ratio as described above can achieve at least two notable effects. 
     First, strain is relaxed, and SiC with less strain can be formed. Compared with a case where co-doping is not performed, strain is smaller, the number of defects is smaller, and larger amounts of impurities can be implanted. That is, the solid solubility limits of impurities can be raised. Accordingly, the sheet resistance, the resistivity, and the contact resistance are lowered. As fewer defects are formed by either ion implantation or epitaxial growth, dosing of large amounts of impurities can be performed. 
     Secondly, shallow levels can be formed. Compared with a case where co-doping is not performed, a low-resistance material can be formed with smaller amounts of impurities. Alternatively, a sheet resistance that is one or more digits lower can be achieved with the same amounts of impurities as those in a case where co-doping is not performed. In a region that can be formed through epitaxial growth and contains a low-dose impurity, the resistance becomes higher unless co-doping is performed. However, low-resistance SiC can be formed when co-doping is performed. Accordingly, a SiC semiconductor device having a lower on-state resistance can be manufactured. 
     In the IGBT  100  of this embodiment, the p-type SiC single-crystal layer  12  is co-doped with a p-type impurity such as Al and an n-type impurity such as N. With this arrangement, the sheet resistance and the resistivity of the p-type SiC single-crystal layer  12  are lowered. Accordingly, a reduction in on-state resistance is achieved, and the high-performance IGBT  100  is realized. 
     As trimers are formed, the crystalline structures are stabilized, and crystal defects are reduced. Accordingly, the IGBT  100  having smaller leakage current is realized. Furthermore, as the crystalline structures are stabilized, the IGBT  100  that has excellent energization breakdown tolerance is realized. That is, the IGBT  100  is highly reliable against deterioration due to energization. 
     As for deterioration due to energization, there is a mode in which crystal defects having 3C structures are formed, and the resistance becomes higher. With the co-doped structure of this embodiment, the crystals are stable, and such a mode does not appear. Accordingly, the IGBT  100  that does not cause the resistance increasing mode to appear can be formed. 
     The concentration of the p-type impurity contained in the p-SiC single-crystal layer  12  is preferably not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 . This is also because, if the concentration is below the range, there is a possibility that interaction between the p-type impurity and the n-type impurity does not easily occur, and trimers are not formed. This is also because it is difficult to incorporate the p-type impurity having a concentration higher than the range. 
     So as to sufficiently lower sheet resistance or resistivity of the p-SiC single-crystal layer  12 , the concentration of the p-type impurity contained in the p-SiC single-crystal layer  12  is preferably 1×10 20  cm −3  or higher. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the p-SiC single-crystal layer  12 , the ratio of the concentration of the element D to the concentration of the element A is higher than 0.33 but lower than 1.0, so as to sufficiently lower the sheet resistance or the resistivity of the third SiC region  20 . Also, the ratio of the concentration of the element D to the concentration of the element A is preferably higher than 0.40 but lower than 0.95. More preferably, the ratio is not lower than 0.45 and not higher than 0.75. Even more preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     Therefore, the ratio of the concentration of the element D to the concentration of the element A in the liquid phase when the p-Sic single-crystal layer  12  is grown is higher than 0.33 but lower than 1.0. Also, the ratio of the concentration of the element D to the concentration of the element A is preferably higher than 0.40 but lower than 0.95. More preferably, the ratio is not lower than 0.45 and not higher than 0.75. Even more preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     The ratio of the concentration of the element D to the concentration of the element A in the p-SiC single-crystal layer  12  can be calculated by determining the respective densities of the element A and the element D by SIMS (Secondary Ion Microprobe Spectrometry), for example. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the p-Sic single-crystal layer  12 , the acceptor levels that contribute to generation of carriers of the element A are preferably 150 meV or shallower, so as to lower sheet resistance or resistivity. More preferably, the acceptor levels are 100 meV or shallower. Even more preferably, the acceptor levels are 40 meV or shallower. 
     The acceptor levels of the element A can be determined by measuring the activation energy of the sheet resistance or the resistivity of the p-SiC single-crystal layer  12 , for example. 
     So as to sufficiently lower the sheet resistance or the resistivity of the p-SiC single-crystal layer  12 , most of the p-type impurity and the n-type impurity preferably forms trimers. Therefore, 90% or more of the element D is preferably in the lattice site locations nearest to the element. A. If 90% or more of the element D is in the lattice site locations nearest to the element A, most of the p-type impurity and the n-type impurity (90% or more of the part that can form trimers) can be considered to form trimers. 
     The proportion of the element D in the lattice site locations nearest to the element A can be determined by analyzing the binding state between the element A and the element D by XPS (X-ray Photoelectron Spectroscopy), for example. 
     When the p-SiC single-crystal layer  12  is grown by a liquid phase growth technique, the p-type impurity and the n-type impurity coexist at the above described predetermined ratio in the liquid phase. Therefore, conversion of TSDs into BPDs during crystal growth is facilitated. Accordingly, TSDs can be prevented from extending into an upper layer from a layer with a smaller thickness than in a case where the p-SiC single-crystal layer  12  is formed by a vapor phase growth technique, for example. Also, with the same thickness, the density of TSDs that reach the surface can be reduced. 
     As described above, according to the method of manufacturing the semiconductor device of this embodiment, the p-SiC single-crystal layer  12  is formed by a liquid phase growth technique. Accordingly, dislocations in a semiconductor layer surface and in a semiconductor layer of the device can be reduced, and a highly-reliable IGBT can be realized. Also, the p-SiC single-crystal layer  12  is co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that on-state resistance is lowered, and a high-performance IGBT is realized. 
     Furthermore, the p-SiC single-crystal layer  12  is formed from a liquid phase co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that conversion of TSDs into BPDs can be facilitated. Accordingly, the thickness of the p-SiC single-crystal layer  12  formed by liquid phase growth can be reduced, and productivity is increased. Also, conversion of TSDs into BPDs is facilitated, so that the density of dislocations that reach the surface can be lowered. 
     Second Embodiment 
     A method of manufacturing a semiconductor device of this embodiment includes: preparing a substrate; and growing a p-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a p-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element D to the concentration of the element A in the first or second combination being higher than 0.33 but lower than 1.0, the concentration of the element A in the combination being not lower than 1×10 16  cm −3  and not higher than 1×10 22  cm −3 . 
     More particularly, the substrate includes an n-type SiC layer. A SiC, single-crystal layer is formed on the surface of the n-type SiC layer. An n-type second SiC region is formed in the surface of the SiC single-crystal layer. A p-type third SiC region is formed in the surface of the SiC single-crystal layer. An n-type fourth SiC region is formed in the surface of the SiC single-crystal layer, the SiC single-crystal layer being interposed between the second SiC region and the fourth SiC region. A gate insulating film is formed on the surfaces of the fourth SiC region and the SiC single-crystal layer. A gate electrode is formed on the gate insulating film. A first electrode connected to the second SiC region and the third SiC region is formed. A second electrode connected to the SiC layer is formed. 
     Explanation of the same aspects as those of the function and effects of the liquid phase growth technique and the co-doping of the first embodiment will not be repeated. Also, explanation of the same aspects as those of the semiconductor device and the method of manufacturing the semiconductor device of the first embodiment will not be repeated. 
       FIG. 17  is a schematic cross-sectional view of the structure of a MOSFET (Metal Oxide Semiconductor Field Effect Transistor) that is a semiconductor device of this embodiment. The MOSFET  200  is an n-type vertical MOSFET that has electrons as carriers. 
     The MOSFET  200  includes a substrate  51 . The substrate  51  includes an n-type SiC substrate (an n-SiC single-crystal substrate)  50  and an n-type SiC layer (an n − -SiC layer)  14  on the surface of the n-SiC single-crystal substrate  50 . The n-SiC single-crystal substrate  50  is a 4H-SiC substrate (an n-substrate) containing N (nitrogen) as the n-type impurity, for example, at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 19  cm −3 , for example. 
     The concentration of the n-type impurity in the n-type SiC layer (the n − -SiC layer)  14  is not lower than 5×10 15  cm −3  and not higher than 2×10 16  cm −3 , for example. The thickness of the n − -SiC layer  14  is not smaller than 5 μm and not greater than 20 μm, for example. 
     A p-type SiC single-crystal layer (a p-SiC single-crystal layer: a p-well region)  76  formed by a liquid phase growth technique is provided on the surface of the n − -SiC layer  14 . This p-type SiC single-crystal layer  76  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element A and the element D form a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus). The ratio of the concentration of the element D to the concentration of the element A in the first or second combination (concentration D/concentration A) is higher than 0.33 but lower than 1.0. In this embodiment, the impurity concentration of the element A is not lower than 1×10 16  cm −3  and not higher than 5×10 17  cm −3 . 
     In the case of the first combination of Al (aluminum), Ga (gallium), or In (indium) and N (nitrogen), for example, the element A may be a single element selected from Al (aluminum), Ga (gallium), and In (iridium). Alternatively, the element A may be formed with two elements such as Al (an element A 1 ) and Ga (an element A 2 ) or may be formed with three elements such as Al (the element A 1 ), Ga (the element A 2 ), and In (an element A 3 ). In a case where the element A is formed with more than one element, the element A may be formed with two or three kinds of elements, as long as the above described conditions on the ratio of the concentration of the element D to the concentration of the element A and on the concentration of the element A are satisfied. 
     The first combination and the second combination can coexist. However, the above described conditions on the ratio of the concentration of the element D to the concentration of the element A and on the concentration of the element A should be satisfied with elements that form at least one of the first and second combinations. In other words, each of the first combination and the second combination should satisfy the conditions on the element ratio and the element concentration. This is because the later described trimers are not formed between an impurity in the first combination and an impurity in the second combination. 
     In a case where the Al concentration is 1×10 17  cm −3 , the Ga concentration is 1×10 17  cm −3 , and the N concentration is 1×10 17  cm −3 , for example, N/(Al+Ga) is 0.5, and (Al+Ga) is 2×10 −7  cm −3 . In this case, the element ratio and the element concentrations are within the ranges set by this embodiment. 
     In a case where the B concentration is 4×10 17  cm −3 , the P concentration is 1×10 17  cm −3 , and the N concentration is 1×10 17  cm −3 , for example, attention is paid only to B and P, which forms the second combination. As a result, P/B is 0.25, which does not satisfy the element ratio condition, and the element ratio is outside the range set by this embodiment. 
     Also, in a case where the Al concentration is 5×10 15  cm −3 , the B concentration is 5×10 15  cm 3 , the N concentration is 2.5×10 15  cm 3 , and the P concentration is 2.5×10 15  cm −3 , N/Al is 0.5, which satisfies the ratio condition, but the Al concentration is lower than 1×10 16  cm −3  in the first combination. In the second combination, P/B is 0.5, which satisfies the ratio condition, but the B concentration is lower than 1×10 16  cm −3 . Therefore, either of the first and second combinations does not satisfy the desirable element concentration condition. 
     It should be noted that this embodiment does not exclude elements other than the above mentioned elements as p-type impurities and n-type impurities. In the following, an example case where the element A is Al (aluminum) and the element N (nitrogen) is described. 
     So as to set an appropriate threshold value in the MOSFET  200 , the Al concentration in the p-SiC single-crystal layer  76  is preferably not lower than 1×10 16  cm −3  and not higher than 5×10 17  cm −3 . The thickness of the p-SiC single-crystal layer  76  is not smaller than 0.3 μm and not greater than 1.0 μm, for example. The p-SiC single-crystal layer  76  functions as the channel region of the MOSFET  200 . 
     An n − -type fourth SiC region (a JFET region)  17  containing the n-type impurity at an impurity concentration that is not lower than 5×10 15  cm −3  and not higher than 1×10 19  cm −3 , for example, is formed in part of the surface of the p-SiC single-crystal layer  76 . The depth of the JFET region  17  is equal to or greater than the thickness of the p-SiC single-crystal layer  76 . The JFET region  17  is connected to the n − -SiC layer  14 . The JFET region  17  functions as a transfer path for electrons serving as carriers. 
     An n + -type second SiC region (a source region)  18  containing the n-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the p-SiC single-crystal layer  76 . The depth of the source region  18  is smaller than the thickness of the p-SiC single-crystal layer  76 , and is approximately 0.3 μm, for example. The source region  18  is located at a distance from the JFET region  17 , with the p-SiC single-crystal layer  76  being interposed therebetween. 
     A p + -type third SiC region (a p-well contact region)  20  containing the p-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 cm −3 , for example, is formed in part of the surface of the p-SiC single-crystal layer  76  and on a side of the source region  18 . The depth of the p-well contact region  20  is smaller than the thickness of the p-SiC single-crystal layer  76 , and is approximately 0.3 μm, for example. 
     A gate insulating film  28  is continuously formed on the surfaces of the JFET region  17  and the p-SiC single-crystal layer  76 , so as to extend across those regions. The gate insulating film  28  may be a silicon oxide film (a SiO 2  film), a silicon oxynitride film, or a high-k insulating film, for example. 
     A gate electrode  30  is formed on the gate insulating film  28 . The gate electrode  30  may be made of polysilicon, for example. An interlayer insulating film  32  formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     The p-SiC single-crystal layer  76  interposed between the source region  18  and the JFET region  17  under the gate electrode  30  functions as the channel region of the MOSFET  200 . 
     A conductive first electrode (a source/p-well common electrode)  24  that is electrically connected to the source region  18  and the p-well contact region  20  is provided. The first electrode (the source/p-well common electrode)  24  is formed with a Ni (nickel) barrier metal layer  24   a  and an Al metal layer  24   b  formed on the barrier metal layer  24   a , for example. The Ni barrier metal layer  24   a  and the Al metal layer  24   b  may form an alloy through a reaction. 
     A conductive second electrode (a drain electrode)  36  is formed on the side of the bottom surface of the SiC substrate  51 . The second electrode (the drain electrode)  36  is made of Ni, for example. 
     In this embodiment, the n-type impurity is preferably N (nitrogen) or P (phosphorus), for example, but it is possible to use As (arsenic) or the like. Also, the p-type impurity is preferably Al (aluminum), for example, but it is possible to use B (boron), Ga (gallium), In (indium), or the like. 
     Next, a method of manufacturing the semiconductor device of this embodiment is described. 
       FIG. 18  is a flowchart showing the method of manufacturing the semiconductor device of this embodiment.  FIGS. 19 and 20  are schematic cross-sectional views illustrating the method of manufacturing the semiconductor device of this embodiment. 
     As shown in  FIG. 18 , the method of manufacturing the semiconductor device includes: substrate preparation (step S 202 ); p-SiC single-crystal layer formation (step S 204 ); n-type impurity ion implantation (step S 206 ); p-type impurity ion implantation (step S 208 ); n-type impurity ion implantation (step S 209 ); annealing (step S 210 ); gate insulating film formation (step S 212 ); gate electrode formation (step S 214 ); interlayer film formation (step S 216 ); first electrode formation (step S 218 ); second electrode formation (step S 220 ); and annealing (step S 222 ). 
     First, in step S 202 , the 4H-SiC n-type SiC substrate (the n-SiC single-crystal substrate)  50  that contains P (phosphorus) or N (nitrogen) as the n-type impurity at an impurity concentration of approximately 5×10 18  cm −3 , has low resistance, and has a thickness of 300 μm, for example, is prepared. 
     The high-resistance n-type SiC epitaxial layer (the n − -SiC layer)  14  that contains N as the n-type impurity at an impurity concentration of approximately 1×10 16  cm 3 , for example, and has a thickness of approximately 10 μm is epitaxially grown on the surface of the n-SiC single-crystal substrate  50  by an epitaxial growth technique. In this manner, the substrate  51  having the n − -SiC layer  14  on the surface of the n-SiC single-crystal substrate  50  is prepared. 
     In step S 204 , the p-type SiC single-crystal layer (the p-SiC single-crystal layer)  76  is formed on the surface of the n − -SiC layer  14  through epitaxial growth by a liquid phase growth technique ( FIG. 19 ). The p-SiC single-crystal layer  76  contains the p-type impurity and the n-type impurity. The method of forming the co-doped p-SiC single-crystal layer  76  by a liquid phase growth technique is the same as that of the first embodiment, except for the impurity ratio. 
     The surface of the n − -SiC layer  14  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. More preferably, the off angle is not smaller than 2 degrees and not larger than 6 degrees. 
     The Al concentration in the p-SiC single-crystal layer  76  is not lower than 1×10 16  cm −3  and not higher than 5×10 17  cm −3 , for example. The concentrations of the p-type impurity and the n-type impurity in the p-SiC single-crystal layer  76  can be adjusted to desired values by controlling the concentrations of the p-type impurity and the n-type impurity Ii) in a liquid phase  1 . 
     In step S 206 , the n + -type second SiC region (the source region)  18  is formed in the same manner as the second emitter region formation of the first embodiment. In step S 208 , the p + -type third SiC region (the p-well contact region)  20  is formed in the same manner as the emitter contact region formation of the first embodiment. 
     After that, patterning is performed by photolithography and etching, to form a mask material  48  made of SiO 2 , for example. In step S 209 , ions of N as the n-type impurities are implanted into the p-type SiC single-crystal layer (the p-SiC single-crystal layer)  76  by using the mask material  48  as the ion implantation mask, to form the n-type fourth SiC region (the JFET region)  17  ( FIG. 20 ). 
     That is, the n-type impurity at a higher concentration than the p-type impurity concentration in the p-well region  16  are implanted through ion implantation, to switch the conductivity types. The accelerating energy and the dose amount in the ion implantation are adjusted so that the depth of the fourth SiC region (the JFET region)  17  becomes equal to or greater than the thickness of the second SiC epitaxial layer. 
     In step S 210 , after the JFET region  17  is formed, annealing for activation is performed. The conditions for the annealing are that an argon (Ar) gas is used as the atmosphere gas, the heating temperature is 1600° C., and the heating period is 30 minutes, for example. At this point, the impurities implanted into the SiC can be activated, but diffusion is small. 
     In step S 212 , the gate insulating film  28  that is formed with a SiO 2  film, for example, is formed by CVD (Chemical Vapor Deposition) or thermal oxidation. In step S 214 , the gate electrode  30  that is made of polysilicon, for example, is formed on the gate insulating film  28 . In step S 216 , the interlayer insulating film  32  that is formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     In step S 218 , the conductive first electrode (the source/p-well common electrode)  24  that is electrically connected to the source region  18  and the p-well contact region  20  is formed. The first electrode (the source/p-well common electrode)  24  is formed by Ni (nickel) and Al sputtering, for example. 
     In step S 220 , the conductive second electrode (the drain electrode)  36  is formed on the side of the bottom surface of the substrate  51 . The second electrode (the drain electrode)  36  is formed by Ni sputtering, for example. 
     In step S 222 , annealing is performed to lower the contact resistance between the first electrode  24  and the second electrode  36 . The annealing is performed in an argon gas atmosphere at 1000° C., for example. 
     By the above described manufacturing method, the MOSFET  200  shown in  FIG. 17  is formed. 
     In this embodiment, the p-type SiC single-crystal layer (the p-SiC single-crystal layer: the p-well region)  76  is formed on the surface of the substrate  51  by using a liquid phase growth technique. With the liquid phase growth technique, TSDs are converted into basal plane dislocations (BPDs) in the p-SiC single-crystal layer  76 . BPDs extend along the {0001} plane, and exit the p-SiC single-crystal layer  76  from a side surface. In this manner, the TSDs are restrained from reaching the surface of the p-SiC single-crystal layer  76 . Accordingly, the reliability of the gate insulating film  28  formed on the surface of the p-SiC single-crystal layer  76  is increased. 
     In the MOSFET  200  manufactured by the manufacturing method according to this embodiment, the p-type SiC single-crystal layer (the p-SiC single-crystal layer: the p-well region)  76  is co-doped with Al and N. The ratio of the N concentration to the Al concentration is higher than 0.33 but lower than 1.0. 
     In this embodiment, the impurity concentrations in the p-SiC single-crystal layer  76  to be the channel region can be adjusted by impurity doping at the time of epitaxial growth. Accordingly, there is no need to implant ions into the channel region so as to adjust the threshold value of the MOSFET  200 . As a result, defects due to ion implantation are not formed. Accordingly, electron scattering due to ion implantation defects does not occur. Thus, the electron mobility in the channel region becomes higher, and a sophisticated MOSFET is realized. 
     Also, as doping of the p-type impurity and the n-type impurity is performed at an appropriate ratio, trimer formation is facilitated. Accordingly, strain and defects in the channel region are reduced. Thus, the electron mobility in the channel region becomes higher, and the sophisticated MOSFET  200  is realized. 
     Also, the solid solubility limit of the p-type impurity becomes higher by virtue of the co-doping. As a result, the p-type impurity concentration in the channel region required to achieve a predetermined threshold value can be lower than that in a case where co-doping is not performed. Accordingly, electron scattering due to an impurity can be reduced. Thus, the electron mobility in the channel region becomes higher, and the sophisticated MOSFET  200  is realized. 
     So as to facilitate trimer formation and set an appropriate threshold value in the MOSFET  200 , the concentration of the p-type impurity is preferably not lower than 1×10 16  cm −3  and not higher than 5×10 17  cm −3 . 
     In this embodiment, the ratio of the concentration of the element D to the concentration of the element A in the formed p-SiC single-crystal layer  76  is preferably higher than 0.40 but lower than 0.95. This is because a high solid solubility limit of the p-type impurity can be secured. Also, the acceptor levels of the element A are preferably equal to or shallower than 150 meV. This is because the resistance of the channel region will become even lower, and the on-state current in the MOSFET  200  will increase. Further, 90% or more of the element D is preferably in the lattice site locations nearest to the element A. This is because most of the p-type impurity and the n-type impurity (90% or more of the impurities that can form trimers) will form trimers, and have a high solid solubility limit and a low resistance. 
     In the p-well contact region  20 , the p-type impurity (Al)) the p-SiC single-crystal layer  76  exists in the background in the first place. Accordingly, the dose amount of the p-type impurity for the ion implantation for forming the p-well contact region  20  can be reduced. Thus, the ion implantation time can be shortened, and lattice damage due to ion implantation can be reduced. 
     Also, the crystal defects due to the thermal stress generated at the time of the annealing for activating the p-type impurity and at the time of the cooling after that, particularly basal plane dislocations, can be prevented from degrading the forward characteristics of the body diode of the MOSFET  200 . Thus, a highly-reliable MOSFET is realized. 
     In the JFET region  17 , the n-type impurity (N) of the p-SiC single-crystal layer  76  exists in the background in the first place. Accordingly, the dose amount of the n-type impurity for the ion implantation for forming the JFET region  17  can be reduced. Thus, the ion implantation time can be shortened, and lattice damage due to ion implantation can be reduced. 
     In a case where the p-type impurity (a second p-type impurity) is an element A while the n-type impurity (a second n-type impurity) is an element D in the JFET region  17 , the element A and the element D preferably form a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a combination of B (boron) and P (phosphorus) The ratio of the concentration of the element A to the concentration of the element D in the first or second combination is preferably higher than 0.40 but lower than 0.95. This is because the trimer formation in the JFET region  17  will be facilitated, and a low-resistance n-layer with fewer defects will be realized. In this case, the concentration of the element D forming part of the above combination is preferably not lower than 1×10 18  cm −3 . 
     When the p-SiC single-crystal layer  76  is grown by a liquid phase growth technique, the p-type impurity and the n-type impurity coexist at the above described predetermined ratio in the liquid phase. Therefore, conversion of TSDs into BPDs during crystal growth is facilitated. Accordingly, TSDs can be prevented from extending into an upper layer from a layer with a smaller thickness than in a case where the p-SiC single-crystal layer  76  is formed by a vapor phase growth technique, for example. Also, with the same thickness, the concentration of TSDs that reach the surface can be reduced. 
     As described above, according to the method of manufacturing the semiconductor device of this embodiment, the p-SiC single-crystal layer  76  is formed by a liquid phase growth technique. Accordingly, dislocations in a semiconductor layer surface and in a semiconductor layer of the device can be reduced, and a highly-reliable MOSFET can be realized. Also, the p-SiC single-crystal layer  76  is co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that electron mobility is increased, on-state resistance is lowered, and a high-performance MOSFET is realized. 
     Furthermore, the p-SiC single-crystal layer  76  is formed from a liquid phase co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that conversion of TSDs into BPDs can be facilitated. Accordingly, the thickness of the p-SiC single-crystal layer  76  formed by liquid phase growth can be reduced, and productivity is increased. Also, conversion of TSDs into BPDs is facilitated, so that the concentration of dislocations that reach the surface can be lowered. 
     Third Embodiment 
     A method of manufacturing a semiconductor device of this embodiment includes: preparing a substrate; and growing a p-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a p-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element D to the concentration of the element A in the first or second combination being higher than 0.33 but lower than 1.0, the concentration of the element A in the combination being not lower than 1×10 16  cm −3  and not higher than 1×10 22  cm −3 . 
     More particularly, the substrate includes an n-type SiC layer and a p-type SiC layer on the n-type SiC layer. A SiC single-crystal layer is formed on the surface of the p-type SiC layer, a first electrode connected to the SiC single-crystal layer is formed, and a second electrode connected to the n-type SiC layer is formed. 
     Explanation of the same aspects as those of the function and effects of the liquid phase growth technique and the co-doping of the first or second embodiment will not be repeated. 
       FIG. 21  is a schematic cross-sectional view of the semiconductor device to be manufactured in this embodiment. This semiconductor device is a mesa-type PiN diode. 
     This PiN diode  300  includes a substrate  81 . The substrate  81  includes an n + -type SIC substrate (a silicon carbide substrate)  82 . The SiC substrate  82  is a 4H-SiC substrate (an n-substrate) that contains N (nitrogen) as the n-type impurity, for example, at an impurity concentration of approximately 5×10 18  to 1×10 19  cm −3 . The surface thereof is a plane inclined at 4 degrees to the {0001} plane, for example. 
     An n-type SiC layer (a buffer layer)  84  having a N concentration that is not lower than 1×10 18  cm −3  and not higher than 5×10 18  cm −3 , for example, is formed on the surface of the SiC substrate  82 . The thickness of the n-type SiC layer  84  is not smaller than 0.5 μm and not greater than 3 μm, for example. 
     An n − -type SiC layer  86  having a N impurity concentration that is not lower than 1×10 15  cm 3  and not higher than 2×10 16  cm −3 , for example, is formed on the n-type SiC layer  84 . The thickness of the n − -type SiC layer  86  is not smaller than 5 μm and not greater than 50 μm, for example. 
     A p-type SiC layer  88  having an Al impurity concentration that is not lower than 1×10 17  cm 3  and not higher than 1×10 18  cm −3 , for example, is provided on the surface of the n-type SiC layer  86 . The p-type SiC layer  88  is co-doped with N (nitrogen) and Al (aluminum). The ratio of the N concentration to the Al concentration is higher than 0.33 but lower than 1.0. The thickness of the p-type SiC layer  88  is not smaller than 0.5 μm and not greater than 3 μm, for example. 
     A p-type SiC single-crystal layer (a p-SiC single-crystal layer)  90  formed by a liquid phase growth technique is provided on the surface of the p-type SiC layer  88 . The p-Sic single-crystal layer  90  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is the element A and the n-type impurity is the element D, the element A and the element D form a combination of Al (aluminum), Ga (gallium), or In (indium) and N (nitrogen), and/or a combination of B (boron) and P (phosphorus). The ratio (concentration D/concentration A) of the concentration of the element D to the concentration of the element A in the above combination is higher than 0.33 but lower than 1.0. In the following, an example case where the element A is Al and the element D is N is described. 
     The Al concentration in the p-SiC single-crystal layer  90  is not lower than 1×10 19  cm −3  and not higher than 1×10 22  cm −3 , for example. The thickness of the p-SiC single-crystal layer  90  is not smaller than 0.1 μm and not greater than 1 μm, for example. 
     A conductive anode electrode  94  that is electrically connected to the p-Sic single-crystal layer  90  is provided. The anode electrode  94  is formed with a Ni (nickel) barrier metal layer  94   a  and an Al metal layer  94   b  formed on the barrier metal layer  94   a , for example. 
     A conductive cathode electrode  96  is formed on the side of the bottom surface of the n + -type SiC substrate  82 . The cathode electrode  96  is made of Ni, for example. 
     Next, an example of a method of manufacturing the PiN diode  300  is described. 
       FIG. 22  is a flowchart showing an example of the method of manufacturing the semiconductor device of this embodiment.  FIGS. 23 and 24  are schematic cross-sectional views illustrating the method of manufacturing the semiconductor device of this embodiment. 
     As shown in  FIG. 22 , the method of manufacturing the semiconductor device includes: substrate preparation (step S 302 ); p + -SiC single-crystal layer formation (step S 304 ); mesa structure formation (step S 306 ); first electrode formation (step S 308 ); second electrode formation (step S 310 ); and annealing (step S 312 ). 
     First, in step S 302 , the substrate  81  is prepared. The substrate  81  is formed by the manufacturing method described below, for example. 
     The n-type SiC layer  84  having a thickness of 1 μm, for example, is formed by epitaxial growth from a vapor phase on the n + -type SiC substrate  82  having an n-type impurity concentration of 5×10 18  cm −3 . The n − -type SiC layer  86  having a thickness of 40 μm, for example, is formed on the n-type SiC layer  84  by epitaxial growth from a vapor phase. 
     The p-type SiC layer  88  having a thickness of 1.5 μm, for example, is formed on the n − -type SiC layer  86  by epitaxial growth from a vapor phase. 
     In step S 304 , the p + -type SiC single-crystal layer (p + -SiC single-crystal layer)  90  is formed on the surface of the p-type SiC layer  88  through epitaxial growth by a liquid phase growth technique ( FIG. 23 ). The p + -SiC single-crystal layer  90  contains the p-type impurity and the n-type impurity. The method of forming the co-doped p + -SiC single-crystal layer  90  by a liquid phase growth technique is the same as that of the first embodiment, except for the substrate preparation. 
     The surface of the substrate  81  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. More preferably, the off angle is not smaller than 2 degrees and not larger than 6 degrees. 
     The Al concentration in the formed p + -SiC single-crystal layer  90  is not lower than 1×10 19  cm −3  and not higher than 1×10 22  cm −3 , for example. The concentrations of the p-type impurity and the n-type impurity in the p + -SiC single-crystal layer  90  can be adjusted to desired values by controlling the concentrations of the p-type impurity and the n-type impurity in a liquid phase  1 . 
     In step S 306 , the mesa structure is formed by a known process ( FIG. 24 ). In step S 308 , the anode electrode  94  is formed by a known process. In step S 310 , the cathode electrode  96  is formed by a known process. 
     In step S 310 , annealing is performed to lower the contact resistance between the anode electrode  94  and the cathode electrode  96 . The annealing is performed in an argon gas atmosphere at 1000° C., for example. 
     By the above described manufacturing method, the PiN diode  300  shown in  FIG. 21  is formed. 
     In this embodiment, the p + -SiC single-crystal layer  90  is formed on the surface of the substrate  81  by using a liquid phase growth technique. With the liquid phase growth technique, TSDs are converted into basal plane dislocations (BPDs) in the p + -SiC single-crystal layer  90 . BPDs extend along the {0001} plane, and exit the p + -SiC single-crystal layer  90  from a side surface. Accordingly, TSDs in the p + -SiC single-crystal layer  90  decrease. If there are TSDs, the reverse leakage current at the pn junction might become larger. According to this embodiment, the TSD density is lowered, so that reverse leakage current can be reduced. 
     In the PiN diode  300  manufactured by the manufacturing method according to this embodiment, the p + -SiC single-crystal layer  90  is co-doped with Al (aluminum) as the p-type impurity and N (nitrogen) as the n-type impurity at a predetermined ratio. With this arrangement, the resistance of the p + -SiC single-crystal layer  90  and the contact resistance of the anode electrode  94  are lowered. Accordingly, the forward current in the PiN diode  300  can be increased. 
     When the p-SiC single-crystal layer  90  is grown by a liquid phase growth technique, the p-type impurity and the n-type impurity coexist at the above described predetermined ratio in the liquid phase. Therefore, conversion of TSDs into BPDs during crystal growth is facilitated. Accordingly, TSDs can be prevented from extending into an upper layer from a layer with a smaller thickness than in a case where the p-SiC single-crystal layer  90  is formed by a vapor phase growth technique, for example. Also, with the same thickness, the density of TSDs that reach the surface can be reduced. 
     As described above, according to the method of manufacturing the semiconductor device of this embodiment, the p-SiC single-crystal layer  90  is formed by a liquid phase growth technique. Accordingly, dislocations in a semiconductor layer surface and in a semiconductor layer of the device can be reduced, and the PiN diode  300  with high reliability and high performance can be realized. As the p + -SiC single-crystal layer  90  is co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, sheet resistance and contact resistance are lowered, and the PiN diode  300  with a large forward current can be realized. Furthermore, the p + -SiC single-crystal layer  90  is formed from a liquid phase co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that conversion of TSDs into BPDs can be facilitated. Accordingly, the thickness of the p + -SiC single-crystal layer  90  formed by liquid phase growth can be reduced, and productivity is increased. Also, conversion of TSDs into BPDs is facilitated, so that the density of dislocations that reach the surface can be lowered. 
     Fourth Embodiment 
     A method of manufacturing a semiconductor device of this embodiment includes: preparing a substrate; and growing an n-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a b-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element A to the concentration of the element D in the first or second combination being higher than 0.40 but lower than 0.95. 
     More particularly, an n-type SiC layer is formed on the surface of the SiC single-crystal layer through epitaxial growth, a p-type first SiC region is formed in the surface of the n-type SiC layer, an n-type second SiC region is formed in the surface of the first SiC region, a p-type third SiC region is formed in the surface of the first SiC region, a gate insulating film is formed on the surfaces of the SiC layer and the first SiC region, a gate electrode is formed on the gate insulating film, a first electrode connected to the second SiC region and the third SiC region is formed, and a second electrode connected to the SiC single-crystal layer is formed. 
     Explanation of the same aspects as those of the function and effects of the liquid phase growth technique and the co-doping of the first embodiment will not be repeated. Also, explanation of the same aspects as those of the semiconductor device and the method of manufacturing the semiconductor device of the first embodiment will not be repeated. 
       FIG. 25  is a schematic cross-sectional view of the structure of a MOSFET that is a semiconductor device of this embodiment. The MOSFET  400  is an n-type vertical MOSFET that has electrons as carriers. 
     This MOSFET  400  includes an n-type SiC substrate (an n-SiC single-crystal substrate)  50 . The n-SiC single-crystal substrate  50  is a 4H-SiC substrate (an n-substrate) containing N (nitrogen) as the n-type impurity, for example, at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 19  cm −3 , for example. 
     An n-type SiC single-crystal layer (an n-SiC single-crystal layer)  52  formed by a liquid phase growth technique is provided on the surface of the n-SiC single-crystal substrate  50 . The n-type SiC single-crystal layer  52  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element A and the element D form a first combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus). The ratio of the concentration of the element A to the concentration of the element D in the first or second combination is higher than 0.40 but lower than 0.95. In the following, an example case where the element A is Al and the element D is N is described. 
     The N (nitrogen) concentration in the n-SiC single-crystal layer  52  is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example. The thickness of the n-SiC single-crystal layer  52  is not smaller than 1 μm and not greater than 350 μm, for example. 
     An n-type SiC layer (an n − -SiC layer)  14  containing the n-type impurity at an impurity concentration that is not lower than 5×10 14  cm −3  and not higher than 2×10 16  cm −3 , for example, is formed on the surface of the n-SiC single-crystal layer  52 . The thickness of the n − -SiC layer  14  is not smaller than 5 μm and not greater than 20 μm, for example. 
     A p-type first SiC region (a p-well region)  16  containing the p-type impurity at an impurity concentration that is not lower than approximately 5×10 15  cm −3  and not higher than approximately 1×10 17  cm −3 , for example, is formed in part of the surface of the n − -SiC layer  14 . The depth of the p-well region  16  is approximately 0.6 μm, for example. The p-well region  16  functions as the channel region of the MOSFET  400 . 
     An n + -type first SiC region (a source region)  18  containing the n-type impurity at an impurity concentration that is not lower than 1×10 18  cm 3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the n − -SiC layer  14 . The depth of the source region  18  is smaller than the depth of the p-well region  16 , and is approximately 0.3 μm, for example. 
     A p + -type third SiC region (a p-well contact region)  20  containing the p-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the p-well region  16  and on a side of the source region  18 . The depth of the p-well contact region  20  is smaller than the depth of the p-well region  16 , and is approximately 0.3 μm, for example. 
     A gate insulating film  28  is continuously formed on the surfaces of the n − -SiC layer  14  and the p-well region  16 , so as to bridge the space between the layer and the region. The gate insulating film  28  may be a SiO 2  film or a high-k insulating film, for example. 
     A gate electrode  30  is formed on the gate insulating film  28 . The gate electrode  30  may be made of polysilicon, for example. An interlayer insulating film  32  formed with a SiC, film, for example, is formed on the gate electrode  30 . 
     The first SiC region  16  interposed between the second SiC regions (the source regions)  18  and the n − -SiC layer  14  under the gate electrode  30  functions as the channel region of the MOSFET  400 . 
     A conductive first electrode (a source/p-well common electrode)  24  that is electrically connected to the source region  18  and the p-well contact region  20  is provided. The first electrode (the source/p-well common electrode)  24  is formed with a Ni (nickel) barrier metal layer  24   a  and an Al metal layer  24   b  formed on the barrier metal layer  24   a , for example. The Ni barrier metal layer  24   a  and the Al metal layer  24   b  may form an alloy through a reaction. 
     A conductive second electrode (a drain electrode)  36  is formed on the side of the bottom surface of the SiC substrate  50 . The second electrode (the drain electrode)  36  is made of Ni, for example. 
     In this embodiment, the n-type impurity is preferably N (nitrogen) or P (phosphorus), for example, but it is possible to use As (arsenic) or the like. Also, the p-type impurity is preferably Al (aluminum), for example, but it is possible to use B (boron), Ga (gallium), In (indium), or the like. 
     Next, a method of manufacturing the semiconductor device of this embodiment is described. 
       FIG. 26  is a flowchart showing an example of the method of manufacturing the semiconductor device of this embodiment.  FIGS. 27 ,  28 , and  29  are schematic cross-sectional views illustrating the method of manufacturing the semiconductor device of this embodiment. 
     As shown in  FIG. 26 , the method of manufacturing the semiconductor device includes: n-SiC single-crystal substrate preparation (step S 400 ); n-SiC single-crystal layer formation by a liquid phase growth technique (step S 401 ); n − -SiC layer formation (step S 402 ); p-type impurity ion implantation (step S 404 ); n-type impurity ion implantation (step S 406 ); p-type impurity ion implantation (step S 408 ); annealing (step S 410 ); gate insulating film formation (step S 412 ); gate electrode formation (step S 414 ); interlayer film formation (step S 416 ); first electrode formation (step S 418 ); second electrode formation (step S 420 ); and annealing (step S 422 ). 
     First, in step S 400 , the 4H-SiC n-type SiC single-crystal substrate (the n-SiC single-crystal substrate)  50  that contains N (nitrogen) as the n-type impurity at an impurity concentration of approximately 5×10 18  cm −3 , has low resistance, and has a thickness of 200 μm, for example, is prepared. 
     In step S 401 , the n-type SiC single-crystal layer (the n-SiC single-crystal layer)  52  is formed on the surface of the n-SiC single-crystal substrate  50  through epitaxial growth by a liquid phase growth technique ( FIG. 27 ). The surface of the n-SiC single-crystal substrate  50  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. More preferably, the off angle is not smaller than 2 degrees and not larger than 6 degrees. 
     The n-type SiC single-crystal layer  52  contains the b-type impurity and the n-type impurity. The method of forming the co-doped n-type SiC single-crystal layer  52  by a liquid phase growth technique is the same as that of the first embodiment, except for the impurity ratio. 
     In step S 402 , the high-resistance n − -SiC layer  14  that contains N as the n-type impurity at an impurity concentration of approximately 1×10 16  cm −3 , for example, and has a thickness of approximately 10 μm is grown on the surface of the n-SiC single-crystal layer  52  by an epitaxial growth technique ( FIG. 28 ). 
     In step S 404 , the p-type first SiC region (the p-well region)  16  is formed in the same manner as the first emitter region formation of the first embodiment. In step S 406 , the n + -type second SiC region (the source region)  18  is formed in the same manner as the second emitter region formation of the first embodiment. In step S 408 , the p + -type third SiC region (the p-well contact region)  20  is formed in the same manner as the emitter contact region formation of the first embodiment. 
     In step S 410 , annealing for activation is performed. The conditions for the annealing are that an argon (Ar) gas is used as the atmosphere gas, the heating temperature is 1600° C., and the heating period is 30 minutes, for example. At this point, the impurities implanted into the SiC can be activated, but diffusion is small. 
     In step S 412 , the gate insulating film  28  that is formed with a SiO 2  film, for example, is formed by CVD (Chemical Vapor Deposition) or thermal oxidation. In step S 414 , the gate electrode  30  that is made of polysilicon, for example, is formed on the gate insulating film  28 . In step S 416 , the interlayer insulating film  32  that is formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     In step S 418 , the conductive first electrode (the source/p-well common electrode)  24  that is electrically connected to the source region  18  and the b-well contact region  20  is formed. The first electrode (the source/p-well common electrode)  24  is formed by Ni (nickel)) and Al sputtering, for example. 
     In step S 420 , the conductive second electrode (the drain electrode)  36  is formed on the side of the bottom surface of the substrate  51 . The second electrode (the drain electrode)  36  is formed by Ni sputtering, for example. 
     In step S 422 , annealing is performed to lower the contact resistance between the first electrode  24  and the second electrode  36 . The annealing is performed in an argon gas atmosphere at 1000° C., for example. 
     By the above described manufacturing method, the MOSFET  400  shown in  FIG. 25  is formed. 
     In this embodiment, the n-SiC single-crystal layer  52  is formed on the surface of the n-SiC single-crystal substrate  50  by using a liquid phase growth technique. With the liquid phase growth technique, TSDs are converted into basal plane dislocations (BPDs) in the n-SiC single-crystal layer  52 . BPDs extend along the {0001} plane, and exit the n-SiC single-crystal layer  52  from a side surface. In this manner, the TSDs are restrained from reaching the surface of the n − -SiC layer  14 . Accordingly, the reliability of the gate insulating film  28  formed on the surface of the n − -SiC layer  14  is increased. 
     The BPD density in the n − -SiC layer  14  can also be lowered. Accordingly, degradation of the forward characteristics of the body diode can be restrained. Thus, a highly-reliable MOSFET is realized. 
     In the MOSFET  400  of this embodiment, the n-SiC single-crystal layer  52  is co-doped with a p-type impurity such as Al and an n-type impurity such as N. With this arrangement, the sheet resistance and the resistivity of the n-SiC single-crystal layer  52  are lowered. Accordingly, a reduction in on-state resistance is achieved, and the high-performance MOSFET  400  is realized. 
     As trimers are formed, the crystalline structures are stabilized, and crystal defects are reduced. Accordingly, the MOSFET  400  having smaller leakage current is realized. Furthermore, as the crystalline structures are stabilized, the MOSFET  400  that has excellent energization breakdown tolerance is realized. That is, the MOSFET  400  is highly reliable against deterioration due to energization. 
     As for deterioration due to energization, there is a mode in which crystal defects having 3C structures are formed, and the resistance becomes higher. With the co-doped structure of this embodiment, the crystals are stable, and such a mode does not appear. Accordingly, the MOSFET  400  that does not cause the resistance increasing mode to appear can be formed. 
     The concentration of the n-type impurity contained in the n-SiC single-crystal layer  52  is preferably not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 . This is also because, if the concentration is below the range, there is a possibility that interaction between the p-type impurity and the n-type impurity does not easily occur, and trimers are not formed. This is also because it is difficult to incorporate the n-type impurity having a concentration higher than the range. 
     So as to sufficiently lower sheet resistance or resistivity of the n-SiC single-crystal layer  52 , the concentration of the n-type impurity contained in the n-SiC single-crystal layer  52  is preferably 1×10 20  cm −3  or higher. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the n-SiC single-crystal layer  52 , the ratio of the concentration of the element A to the concentration of the element D is higher than 0.40 but lower than 0.95, so as to sufficiently lower the sheet resistance or the resistivity of the n-SiC single-crystal layer  52 , and lower the on-state resistance. Also, the ratio of the concentration of the element A to the concentration of the element D is preferably not lower than 0.45 and not higher than 0.75. More preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     Therefore, the ratio of the concentration of the element A to the concentration of the element D in the liquid phase when the n-SiC single-crystal layer  52  is grown is higher than 0.40 but lower than 0.95. Also, the ratio of the concentration of the element A to the concentration of the element D is preferably not lower than 0.45 and not higher than 0.75. More preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     The ratio of the concentration of the element A to the concentration of the element D in the n-SiC single-crystal layer  52  can be calculated by determining the respective concentrations of the element A and the element D by SIMS (Secondary Ion Microprobe Spectrometry), for example. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the n-SiC single-crystal layer  52 , the donor levels that contribute to generation of carriers of the element D are preferably 40 meV or shallower, so as to lower sheet resistance or resistivity. More preferably, the donor levels are 35 meV or shallower. Even more preferably, the donor levels are 20 meV or shallower. 
     The donor levels of the element D can be determined by measuring the activation energy of the sheet resistance or the resistivity of the n-SiC single-crystal layer  52 , for example. 
     So as to sufficiently lower the sheet resistance or the resistivity of the n-SiC single-crystal layer  52 , and realize low on-state resistance, most of the p-type impurity and the n-type impurity preferably forms trimers. Therefore, 90% or more of the element A is preferably in the lattice site locations nearest to the element D. If 90% or more of the element A is in the lattice site locations nearest to the element D, most of the p-type impurity and the n-type impurity (90% or more of the part that can form trimers) can be considered to form trimers. 
     The proportion of the element A in the lattice site locations nearest to the element D can be determined by analyzing the binding state between the element A and the element D by XPS (X-ray Photoelectron Spectroscopy), for example. 
     When the n-SiC single-crystal layer  52  is grown by a liquid phase growth technique, the p-type impurity and the n-type impurity coexist at the above described predetermined ratio in the liquid phase. Therefore, conversion of TSDs into BPDs during crystal growth is facilitated. Accordingly, TSDs can be prevented from extending into an upper layer from a layer with a smaller thickness than in a case where the n-SiC single-crystal layer  52  is formed by a vapor phase growth technique, for example. Also, with the same thickness, the density of TSDs that reach the surface can be reduced. 
     As described above, according to the method of manufacturing the semiconductor device of this embodiment, the n-SiC single-crystal layer  52  is formed by a liquid phase growth technique. Accordingly, dislocations in a semiconductor layer surface and in a semiconductor layer of the device can be reduced, and a highly-reliable MOSFET can be realized. Also, the n-SiC single-crystal layer  52  is co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that on-state resistance is lowered, and a high-performance MOSFET is realized. Furthermore, the n-SiC single-crystal layer  52  is formed from a liquid phase co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that conversion of TSDs into BPDs can be facilitated. Accordingly, the thickness of the n-SiC single-crystal layer  52  formed by liquid phase growth can be reduced, and productivity is increased. Also, conversion of TSDs into BPDs is facilitated, so that the density of dislocations that reach the surface can be lowered. 
     Fifth Embodiment 
     A method of manufacturing a semiconductor device of this embodiment includes: preparing a substrate; and growing an n-type SiC single-crystal layer on the surface of the substrate from a liquid phase that contains Si (silicon), C (carbon), a p-type impurity, and an n-type impurity, the p-type impurity being an element A, the n-type impurity being an element D, the element A and the element D forming a first combination that is at least one combination selected from Al (aluminum) and N (nitrogen), Ga (gallium) and N (nitrogen), and In (indium) and N (nitrogen), and/or a second combination of B (boron) and P (phosphorus), the ratio of the concentration of the element A to the concentration of the element D in the first or second combination being higher than 0.40 but lower than 0.95. 
     More particularly, the substrate includes an n-type SiC layer, a SiC single-crystal layer is formed on the surface of the n-type SiC layer, a p-type first SiC region is formed in the surface of the SiC single-crystal layer, an n-type second SiC region is formed in the surface of the first SiC region, a p-type third SiC region is formed in the surface of the first SiC region, a gate insulating film is formed on the surfaces of the SiC layer and the first SiC region, a gate electrode is formed on the gate insulating film, a first electrode connected to the second SiC region and the third SiC region is formed, and a second electrode connected to the SiC layer is formed. 
     Explanation of the same aspects as those of the function and effects of the liquid phase growth technique and the co-doping of the first embodiment will not be repeated. Also, explanation of the same aspects as those of the semiconductor devices and the methods of manufacturing the semiconductor devices of the first through fourth embodiments will not be repeated. 
       FIG. 29  is a schematic cross-sectional view of the structure of a MOSFET that is a semiconductor device of this embodiment. The MOSFET  500  is an n-type vertical MOSFET that has electrons as carriers. 
     This MOSFET  500  includes an n-type SiC substrate (an n-SiC single-crystal substrate)  50 . The n-SiC single-crystal substrate  50  is a 4H-SiC substrate (an n-substrate) containing N (nitrogen) as the n-type impurity, for example, at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 19  cm −3 , for example. 
     An n-type SiC layer (an n − -SiC single-crystal layer)  14  formed by a liquid phase growth technique is provided on the surface of the n-SiC single-crystal substrate  50 . The n − -SiC single-crystal layer  14  is co-doped with the p-type impurity and the n-type impurity. Where the p-type impurity is an element A and the n-type impurity is an element D, the element. A and the element D form a combination of Al (aluminum), Ga (gallium), or In (indium) and N (nitrogen), and/or a combination of B (boron) and P (phosphorus). The ratio of the concentration of the element A to the concentration of the element D in the combination is higher than 0.40 but lower than 0.95. In the following, an example case where the element A is Al and the element D is N is described. 
     The N (nitrogen) concentration in the n − -SiC single-crystal layer  14  is not lower than 5×10 15  cm −3  not higher than 2×10 16  cm −3 , for example. The thickness of the n − -SiC single-crystal layer  14  is not smaller than 5 μm and not greater than 20 μm, for example. 
     A p-type first SiC region (a p-well region)  16  containing the p-type impurity at an impurity concentration that is not lower than approximately 5×10 15  cm −3  and not higher than approximately 1×10 17  cm −3 , for example, is formed in part of the surface of the n − -SiC single-crystal layer  14 . The depth of the p-well region  16  is approximately 0.6 μm, for example. The p-well region  16  functions as the channel region of the MOSFET  500 . 
     An n + -type first SiC region (a source region)  18  containing the n-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the n − -SiC single-crystal layer  14 . The depth of the source region  18  is smaller than the depth of the p-well region  16 , and is approximately 0.3 μm, for example. 
     A p + -type third SiC region (a p-well contact region)  20  containing the p-type impurity at an impurity concentration that is not lower than 1×10 18  cm −3  and not higher than 1×10 22  cm −3 , for example, is formed in part of the surface of the p-well region  16  and on a side of the source region  18 . The depth of the p-well contact region  20  is smaller than the depth of the p-well region  16 , and is approximately 0.3 μm, for example. 
     A gate insulating film  28  is continuously formed on the surfaces of the n − -SiC single-crystal layer  14  and the p-well region  16 , so as to bridge the space between the layer and the region. The gate insulating film  28  may be a SiO 2  film or a high-k insulating film, for example. 
     A gate electrode  30  is formed on the gate insulating film  28 . The gate electrode  30  may be made of polysilicon, for example. An interlayer insulating film  32  formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     The first SiC region  16  interposed between the second SiC regions (the source regions)  18  and the n − -SiC single-crystal layer  14  under the gate electrode  30  functions as the channel region of the MOSFET  500 . 
     A conductive first electrode (a source/p-well common electrode)  24  that is electrically connected to the source region  18  and the p-well contact region  20  is provided. The first electrode (the source/p-well common electrode)  24  is formed with a Ni (nickel) barrier metal layer  24   a  and an Al metal layer  24   b  formed on the barrier metal layer  24   a , for example. The Ni barrier metal layer  24   a  and the Al metal layer  24   b  may form an alloy through a reaction. 
     A conductive second electrode (a drain electrode)  36  is formed on the side of the bottom surface of the SiC substrate  50 . The second electrode (the drain electrode)  36  is made of Ni, for example. 
     In this embodiment, the n-type impurity is preferably N (nitrogen) or P (phosphorus), for example, but it is possible to use As (arsenic) or the like. Also, the p-type impurity is preferably Al (aluminum), for example, but it is possible to use B (boron), Ga (gallium), In (indium), or the like. 
     Next, a method of manufacturing the semiconductor device of this embodiment is described. 
       FIG. 30  is a flowchart showing an example of the method of manufacturing the semiconductor device of this embodiment.  FIG. 31  is a schematic cross-sectional view illustrating the method of manufacturing the semiconductor device of this embodiment. 
     As shown in  FIG. 30 , the method of manufacturing the semiconductor device includes: n-SiC single-crystal substrate preparation (step S 500 ); n − -SiC single-crystal layer formation by a liquid phase growth technique (step S 502 ); p-type impurity ion implantation (step S 504 ); n-type impurity ion implantation (step S 506 ); p-type impurity ion implantation (step S 508 ); annealing (step S 510 ); gate insulating film formation (step. S 512 ); gate electrode formation (step S 514 ); interlayer film formation (step S 516 ); first electrode formation (step S 518 ); second electrode formation (step S 520 ); and annealing (step S 522 ). 
     First, in step S 500 , the 4H-SiC n-type SiC single-crystal substrate (the n-SiC single-crystal substrate)  50  that contains N (nitrogen) as the n-type impurity at an impurity concentration of approximately 5×10 18  cm −3 , has low resistance, and has a thickness of 200 μm, for example, is prepared. 
     In step S 502 , the n-type SiC layer (the n − -SiC single-crystal layer)  14  is formed on the surface of the n-SiC single-crystal substrate  50  through epitaxial growth by a liquid phase growth technique ( FIG. 31 ). The surface of the n-SiC single-crystal substrate  50  has an off angle that is not smaller than 0.5 degrees and not larger than 8 degrees with respect to the {0001} plane, for example. More preferably, the off angle is not smaller than 2 degrees and not larger than 6 degrees. 
     The n − -SiC single-crystal layer  14  contains the p-type impurity and the n-type impurity. The method of forming the co-doped n − -SiC single-crystal layer  14  by a liquid phase growth technique is the same as that of the first embodiment, except for the impurity ratio and concentrations. 
     The n − -SiC single-crystal layer  14  contains N as the n-type impurity at an impurity concentration of approximately 1×10 16  cm −3 , for example, and has a thickness of approximately 10 μm. 
     In step S 504 , the p-type first SiC region (the p-well region)  16  is formed in the same manner as the first emitter region formation of the first embodiment. In step S 506 , the n + -type second SiC region (the source region)  18  is formed in the same manner as the second emitter region formation of the first embodiment. In step S 508 , the p + -type third SiC region (the p-well contact region)  20  is formed in the same manner as the emitter contact region formation of the first embodiment. 
     In step S 510 , annealing for activation is performed. The conditions for the annealing are that an argon (Ar) gas is used as the atmosphere gas, the heating temperature is 1600° C., and the heating period is 30 minutes, for example. At this point, the impurities implanted into the SiC can be activated, but diffusion is small. 
     In step S 512 , the gate insulating film  28  that is formed with a SiO 2  film, for example, is formed by CVD (Chemical Vapor Deposition) or thermal oxidation. In step S 514 , the gate electrode  30  that is made of polysilicon, for example, is formed on the gate insulating film  28 . In step S 516 , the interlayer insulating film  32  that is formed with a SiO 2  film, for example, is formed on the gate electrode  30 . 
     In step S 518 , the conductive first electrode (the source/p-well common electrode)  24  that is electrically connected to the source region  18  and the p-well contact region  20  is formed. The first electrode (the source/p-well common electrode)  24  is formed by Ni (nickel) and Al sputtering, for example. 
     In step S 520 , the conductive second electrode (the drain electrode)  36  is formed on the side of the bottom surface of the substrate  51 . The second electrode (the drain electrode)  36  is formed by Ni sputtering, for example. 
     In step S 522 , annealing is performed to lower the contact resistance between the first electrode  24  and the second electrode  36 . The annealing is performed in an argon gas atmosphere at 1000° C., for example. 
     By the above described manufacturing method, the MOSFET  500  shown in  FIG. 29  is formed. 
     In this embodiment, the n − -SiC single-crystal layer  14  is formed on the surface of the n-SiC single-crystal substrate  50  by using a liquid phase growth technique. With the liquid phase growth technique, TSDs are converted into basal plane dislocations (BPDs) in the n − -SiC single-crystal layer  14 . BPDs extend along the {0001} plane, and exit the n − -SiC single-crystal layer  14  from a side surface. In this manner, the TSDs are restrained from reaching the surface of the n − -SiC single-crystal layer  14 . Accordingly, the reliability of the gate insulating film  28  formed on the surface of the n − -SiC single-crystal layer  14  is increased. 
     The BPD density in the n-SiC single-crystal layer  14  can also be lowered. Accordingly, degradation of the forward characteristics of the body diode of the MOSFET  500  can be restrained. Thus, a highly-reliable MOSFET is realized. 
     In the MOSFET  500  of this embodiment, the n − -SiC single-crystal layer  14  is co-doped with a p-type impurity such as Al and an n-type impurity such as N. With this arrangement, the sheet resistance and the resistivity of the n − -SiC single-crystal layer  14  are lowered. Accordingly, a reduction in on-state resistance is achieved, and the high-performance MOSFET  500  is realized. 
     As trimers are formed, the crystalline structures are stabilized, and crystal defects are reduced. Accordingly, the MOSFET  500  having smaller leakage current is realized. Furthermore, as the crystalline structures are stabilized, the MOSFET  500  that has excellent energization breakdown tolerance is realized. That is, the MOSFET  500  is highly reliable against deterioration due to energization. 
     As for deterioration due to energization, there is a mode in which crystal defects having 3C structures are formed, and the resistance becomes higher. With the co-doped structure of this embodiment, the crystals are stable, and such a mode does not appear. Accordingly, the MOSFET  500  that does not cause the resistance increasing mode to appear can be formed. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the n − -SiC single-crystal layer  14 , the ratio of the concentration of the element A to the concentration of the element D is higher than 0.40 but lower than 0.95, so as to sufficiently lower the sheet resistance or the resistivity of the n − -SiC single-crystal layer  14 , and lower the on-state resistance. Also, the ratio of the concentration of the element A to the concentration of the element D is preferably not lower than 0.45 and not higher than 0.75. More preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     Therefore, the ratio of the concentration of the element A to the concentration of the element D in the liquid phase when the n − -SiC single-crystal layer  14  is grown is higher than 0.40 but lower than 0.95. Also, the ratio of the concentration of the element A to the concentration of the element D is preferably not lower than 0.45 and not higher than 0.75. More preferably, the ratio is not lower than 0.47 and not higher than 0.60. 
     The ratio of the concentration of the element A to the concentration of the element D in the n − -SiC single-crystal layer  14  can be calculated by determining the respective concentrations of the element A and the element D by SIMS (Secondary Ion Microprobe Spectrometry), for example. 
     In a case where the p-type impurity is the element A and the n-type impurity is the element D in the n − -SiC single-crystal layer  14 , the donor levels that contribute to generation of carriers of the element D are preferably 90 meV or shallower, so as to lower sheet resistance or resistivity. More preferably, the donor levels are 35 meV or shallower. Even more preferably, the donor levels are 20 meV or shallower. 
     The donor levels of the element D can be determined by measuring the activation energy of the sheet resistance or the resistivity of the n − -SiC single-crystal layer  14 , for example. 
     So as to sufficiently lower the sheet resistance or the resistivity of the n − -SiC single-crystal layer  14 , and realize low on-state resistance, most of the p-type impurity and the n-type impurity preferably forms trimers. Therefore, 90% or more of the element A is preferably in the lattice site locations nearest to the element D. If 90% or more of the element A is in the lattice site locations nearest to the element D, most of the p-type impurity and the n-type impurity (90% or more of the part that can form trimers) can be considered to form trimers. 
     The proportion of the element A in the lattice site locations nearest to the element D can be determined by analyzing the binding state between the element A and the element D by XPS (X-ray Photoelectron Spectroscopy), for example. 
     When the n − -SiC single-crystal layer  14  is grown by a liquid phase growth technique, the p-type impurity and the n-type impurity coexist at the above described predetermined ratio in the liquid phase. Therefore, conversion of TSDs into BPDs during crystal growth is facilitated. Accordingly, TSDs can be prevented from extending into an upper layer from a layer with a smaller thickness than in a case where the n − -SiC single-crystal layer  14  is formed by a vapor phase growth technique, for example. Also, with the same thickness, the density of TSDs that reach the surface can be reduced. 
     As described above, according to the method of manufacturing the semiconductor device of this embodiment, the n − -SiC single-crystal layer  14  is formed by a liquid phase growth technique. Accordingly, dislocations in a semiconductor layer surface and in a semiconductor layer of the device can be reduced, and a highly-reliable MOSFET can be realized. Also, the n − -SiC single-crystal layer  14  is co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that on-state resistance is lowered, and a high-performance MOSFET is realized. Furthermore, the n − -SiC single-crystal layer  14  is formed from a liquid phase co-doped with the p-type impurity and the n-type impurity at a predetermined ratio, so that conversion of TSDs into BPDs can be facilitated. Also, conversion of TSDs into BPDs is facilitated, so that the density of dislocations that reach the surface can be lowered. 
     Although silicon carbide crystalline structures are 4H-SiC in the above described embodiments, the embodiments can also be applied to silicon carbides having other crystalline structures such as 6H-SiC and 3C-SiC. 
     Although the substrate for forming a SiC single-crystal layer thereon by a liquid phase growth technique is a SiC substrate in each of the above described examples, a single-crystal substrate other than a SiC substrate can also be used, as long as epitaxial growth is possible on the single-crystal substrate. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, a method of manufacturing a semiconductor device described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the devices and methods described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.