Patent Publication Number: US-6911351-B2

Title: Method of fabricating nitride semiconductor, method of fabricating nitride semiconductor device, nitride semiconductor device, semiconductor light emitting device and method of fabricating the same

Description:
CROSS-REFERENCED TO RELATED APPLICATIONS 
     This application is a Divisional of application Ser. No. 09/712,127 filed Nov. 15, 2000, now U.S. Pat. No. 6,720,586 issued Apr. 13, 2004. 
    
    
     BACKGROUND OF THE INVENTION 
     The present invention relates to a method of fabricating a nitride semiconductor for use in a short-wavelength semiconductor laser diode and the like expected to be applied to the fields of optical information processing and the like, a semiconductor device and a semiconductor light emitting device using the nitride semiconductor and a method of fabricating the same. 
     Recently, a nitride semiconductor of a group III-V compound, that is, a group V element including nitride (N), is regarded as a promising material for a short-wavelength light emitting device due to its large energy gap. In particular, a gallium nitride-based compound semiconductor (Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1) has been earnestly studied and developed, resulting in realizing a practical blue or green light emitting diode (LED) device. Furthermore, in accordance with capacity increase of an optical disk unit, a semiconductor laser diode lasing at approximately 400 nm is earnestly desired, and a semiconductor laser diode using a gallium nitride-based semiconductor is to be practically used. 
     CONVENTIONAL EXAMPLE 1 
     Now, a gallium nitride-based semiconductor laser diode according to Conventional Example 1 will be described with reference to drawings. 
       FIG. 37  shows the sectional structure of the conventional gallium nitride-based semiconductor laser diode showing laser action. As is shown in  FIG. 37 , the conventional semiconductor laser diode includes a buffer layer  302  of gallium nitride (GaN), an n-type contact layer  303  of n-type GaN, an n-type cladding layer  304  of n-type aluminum gallium nitride (AlGaN), an n-type light guiding layer  305  of n-type GaN, a multiple quantum well (MQW) active layer  306  including gallium indium nitride layers having different composition ratios of indium (Ga 1-x In x N/Ga 1-y In y N, wherein 0&lt;y&lt;x&lt;1), a p-type light guiding layer  307  of p-type GaN, a p-type cladding layer  308  of p-type AlGaN and a p-type contact layer  309  of p-type GaN successively formed on a substrate  301  of sapphire by, for example, metal organic vapor phase epitaxial growth (MOVPE). 
     An upper portion of the p-type cladding layer  308  and the p-type contact layer  309  is formed into a ridge with a width of approximately 3 through 10 μm. A lamination body including the MQW active layer  306  is etched so as to expose part of the n-type contact layer  303 , and the upper face and the side faces of the etched lamination body are covered with an insulating film  310 . In a portion of the insulating film  310  above the p-type contact layer  309 , a stripe-shaped opening is formed, a p-side electrode  311  in ohmic contact with the p-type contact layer  309  through the opening is formed over a portion of the insulating film  310  above the ridge. Also, on a portion of the n-type contact layer  303  not covered with the insulating film  310 , an n-side electrode  312  in ohmic contact with the n-type contact layer  303  is formed. 
     In the semiconductor laser diode having the aforementioned structure, when a predetermined voltage is applied to the p-side electrode  311  with the n-side electrode  312  grounded, optical gain is generated within the MQW active layer  306 , so as to show laser action at a wavelength of approximately 400 nm. 
     The wavelength of laser action depends upon the composition ratios x and y or the thicknesses of the Ga 1-x In x N and Ga 1-y In y N layers included in the MQW active layer  306 . At present, the laser diode having this structure has been developed to show continuous laser action at room temperature or more. 
     Furthermore, laser action in the fundamental mode of the lateral mode along a horizontal direction (parallel to the substrate surface) can be shown by adjusting the width or height of the ridge. Specifically, the laser action of the fundamental lateral mode can be shown by providing a difference in the light confinement coefficient between the fundamental lateral mode and a primary or higher mode. 
     The substrate  301  is formed from, apart from sapphire, silicon carbide (SiC), neodymium gallate (NdGaO 3 ) or the like, and any of these materials cannot attain lattice match with gallium nitride and is difficult to attain coherent growth. As a result, any of these materials includes a large number of mixed dislocations, namely, mixed presence of edge dislocations, screw dislocations and other dislocations. For example, when the substrate is made from sapphire, the substrate includes dislocations at a density of approximately 1×10 9  cm −2 , which degrades the reliability of the semiconductor laser diode. 
     As a method for reducing the density of dislocations, epitaxial lateral overgrowth (ELOG) has been proposed. This is an effective method for reducing threading dislocations in a semiconductor crystal with large lattice mismatch. 
     CONVENTIONAL EXAMPLE 2 
       FIG. 38  schematically shows the distribution of crystal dislocations in a semiconductor layer of gallium nitride formed by the ELOG. 
     The outline of the ELOG will be described with reference to FIG.  38 . First, a seed layer  402  of GaN is grown on a substrate  401  of sapphire by the MOVPE or the like. 
     Next, a dielectric film of silicon oxide or the like is deposited by chemical vapor deposition (CVD) or the like, and the deposited dielectric film is formed into a mask film  403  having an opening pattern in the shape of stripes with a predetermined cycle by photolithography and etching. 
     Then, a semiconductor layer  404  of GaN is formed on the mask film  403  by selective growth with portions of the seed layer  402  exposed from the mask film  403  used as a seed crystal by the MOVPE or halide vapor phase epitaxial growth. 
     At this point, although a dislocation high-density region  404   a  where the dislocation density is approximately 1×10 9  cm −2  is formed in a portion of the semiconductor layer  404  above the opening of the mask film  403 , a dislocation low-density region  404   b  where the dislocation density is approximately 1×10 7  cm −2  can be formed in a portion of the semiconductor layer  404  laterally grown on the mask film  403 . 
       FIG. 39  shows the sectional structure of a semiconductor laser diode whose active area, namely, a ridge working as a current injecting region, is formed above the dislocation low-density region  404   b . In  FIG. 39 , like reference numerals are used to refer to like elements shown in  FIGS. 37 and 38 . 
     When the current injecting region is formed above the dislocation low-density region  404   b  of the MQW active layer  306  in this manner, the reliability of the laser diode can be improved. 
     As a result of various examinations, the present inventors have found that semiconductor laser diodes according to Conventional Examples 1 and 2 have the following problems: 
     First, the problems of the growth method of a nitride semiconductor by the ELOG according to Conventional Example 2 will be described. 
     FIGS.  40 ( a ) through  40 ( d ) schematically show a state where polycrystals  405  of gallium nitride are deposited on the mask film  403  during the growth of the semiconductor layer  404  so as to degrade the crystallinity of the semiconductor layer  404 . 
     Specifically, the mask film  403  having the openings is first formed on the seed layer  402  as is shown in FIG.  40 ( a ), and plural semiconductor layers  404  are respectively grown by using, as the seed crystal, the portions of the seed layer  402  exposed in the openings of the mask film  403  as is shown in FIG.  40 ( b ). At this point, since the mask film  403  is formed from a dielectric, plural polycrystals  405  that cannot be crystallized on a dielectric may be deposited on the mask film  403 . 
     Next, as is shown in FIGS.  40 ( c ) and  40 ( d ), when the plural semiconductor layers  404  are grown to be integrated and to have a flat face with the polycrystals  405  deposited, a region  404   c  with poor crystallinity is formed on each polycrystal  405 . 
     The present inventors have found that a laser diode with good characteristics cannot be obtained when the current injecting region is formed above the region  404   c  with poor crystallinity. 
     Second, the present inventors have found a problem that, in the semiconductor laser diode according to Conventional Example 1 or 2, it is difficult to increase the light confinement coefficient of the active layer along a direction vertical to the substrate surface. 
       FIG. 41  shows the relationship, in the semiconductor laser diode of Conventional Example 1, between the distribution of a refractive index of the MQW active layer  306  along the direction vertical to the substrate surface and the distribution of light intensity on a cavity facet. It is understood that part of generated light confined within the MQW active layer  306  leaks to the substrate  301  so as to generate a standing wave in the n-type contact layer  303 . When the generated light is thus largely leaked from the MQW active layer  306  to the substrate  301 , the light confinement ratio in the MQW active layer  306  is lowered, resulting in increasing the threshold value for laser action. 
     Also,  FIG. 42  shows a far-field pattern of the laser diode of Conventional Example 1. In this drawing, the abscissa indicates a shift of emitted light from the normal direction of the cavity facet toward the horizontal direction (along the substrate surface), and the ordinate indicates light intensity of the emitted light. When the generated light is largely leaked to the substrate  301  as in Conventional Example 1, it is also difficult to obtain a unimodal far-field pattern. This goes for the semiconductor laser diode of Conventional Example 2. 
     Thirdly, the semiconductor laser diode of Conventional Example 1 has a problem that, in dividing plural laser diodes formed on a wafer into individual laser chips by, for example, cleavage, the facet of the cavity cannot be flat because the substrate of sapphire and the nitride semiconductor layer have different crystal planes. Specifically, as is shown in  FIG. 43 , sapphire forming the substrate  301  is easily cleaved on the (1-100) surface orientation, namely, the so-called M plane, and hence, the substrate is generally cleaved on the M plane of sapphire. 
     However, the M plane of a nitride semiconductor, for example, gallium nitride is shifted from the M plane of sapphire by 30 degrees in the plane, and hence, the M plane of sapphire accords with the (11-20) surface orientation, namely, the so-called A plane, of gallium nitride. Accordingly, when the substrate  301  is cleaved, cleaved ends of the buffer layer  302  and the lamination body above are shifted from that of the substrate  301  by 30 degrees so as to appear as an irregular face with level differences of several hundreds nm. 
     When the cavity facet is such an irregular face, mirror loss of laser at the cavity facet is increased, so as to increase the operation current of the semiconductor laser diode, which can degrade the reliability of the semiconductor laser diode. Furthermore, since the irregularities are randomly formed on the cavity facet, it is difficult to form with good reproducibility a cavity facet having a predetermined reflectance, which lowers the yield. Even when the cavity is formed not by cleavage but by dry etching, the same problem arises. Herein, a minus sign “−” used in a surface orientation indicates inversion of an index following the minus sign. 
     On the other hand, in the semiconductor laser diode of Conventional Example 2, the stripe-shaped opening of the mask film  403  for the selective growth is formed parallel to the M-axis of the semiconductor layer  404 . This is because a rate of the lateral growth along the A-axis is much higher than in other directions, and hence, the selective growth can be effectively proceeded in a short period of time. Therefore, the dislocation low-density region  404   b  is parallel to the M-axis, and therefore, the cavity facet of the laser diode formed above the dislocation low-density region naturally accords with the M plane. As a result, it is necessary to cleave the substrate  401  on the A plane. Although sapphire can be easily cleaved on the M plane as described above, it cannot be easily cleaved on the A plane, which largely lowers the yield of the semiconductor laser diode. 
     Fourthly, it is known that an angle (tilt) between the C-axis of the seed layer  402  and the C-axis of the semiconductor layer  404  selectively grown above the seed layer  402  is approximately 0.1 through 1 degree in the ELOG. 
     On the other hand, when the ELOG is conducted again by using the dislocation low-density region  404   b  obtained by the ELOG as the seed crystal and covering the dislocation high-density region  404   a  with another mask film for selective growth, a nitride semiconductor crystal can be obtained merely from the dislocation low-density region  404   b . Accordingly, a cavity having a facet according to the A plane can be formed on the crystal formed from merely the dislocation low-density region  404   b , resulting in largely increasing the yield in the cleavage. 
     When the cavity is formed along the A-axis, however, a waveguide is formed in a zigzag manner along the C-axis because of the tilt of the C-axis between the seed layer  402  and the selectively grown layer above the seed layer  402  as described above. Such a zigzag waveguide causes waveguide loss, resulting in a problem of increase of the operation current of the laser diode. Moreover, in a vertical cavity surface emitting laser diode array where plural cavitys are arranged in a direction vertical to the substrate surface, there arises a problem that the directions of emitting laser beams from the respective cavitys in the array do not accord with one another. 
     Fifthly, in the semiconductor laser diode of Conventional Example 2, the width of the dislocation low-density region  404   b  is as small as approximately 5 μm, and it is necessary to align a photomask for the ridge with a width of approximately 3 μm so as not to miss the dislocation low-density region  404   b . Accordingly, high accuracy is required for alignment in the photolithography, which lowers the throughput and the yield in the photolithography. As a result, there arises a problem that productivity cannot be improved. 
     SUMMARY OF THE INVENTION 
     The present invention was devised in consideration of the aforementioned various conventional problems. A first object of the invention is improving crystallinity in ELOG, a second object is increasing a light confinement coefficient of a cavity, a third object is forming a cavity facet with small mirror loss, a fourth object is forming a cavity with small waveguide loss, and a fifth object is easing alignment of a mask for forming a ridge. By achieving these objects, the invention exhibits an excellent effect, in particular, in application to a laser diode for use in an optical disk unit. 
     The first method of fabricating a nitride semiconductor of this invention achieves the fist object and comprises the steps of forming, on a substrate, a first nitride semiconductor layer of Al u Ga v In w N, wherein 0≦u, v, w 1 and u+v+w=1; forming, in an upper portion of the first nitride semiconductor layer, plural convexes extending at intervals along a substrate surface direction; forming a mask film for covering bottoms of recesses formed between the convexes adjacent to each other; and forming, on the first nitride semiconductor layer, a second nitride semiconductor layer of Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1, by using, as a seed crystal, C planes corresponding to top faces of the convexes exposed from the mask film. 
     In the first method of fabricating a nitride semiconductor, the plural convexes are formed in the upper portion of the first nitride semiconductor layer and the bottoms of the recesses sandwiched between the convexes are covered with the mask film. Therefore, the second nitride semiconductor layer is grown by using, as the seed crystal, merely the C planes appearing on the top faces of the convexes of the first nitride semiconductor layer. As a result, even when polycrystals of the second nitride semiconductor layer are deposited on the mask film, the second nitride semiconductor layer grows over the polycrystals in the growth along a direction parallel to the substrate surface (lateral growth) owing to the mask film formed on the bottoms of the recesses between the convexes. Accordingly, the second nitride semiconductor layer is never prevented from growing by the polycrystals, resulting in attaining good crystallinity. 
     The second method of fabricating a nitride semiconductor of this invention achieves the first object and comprises the steps of forming, on a substrate, a first nitride semiconductor layer of Al u Ga v In w N, wherein 0≦u, v, w≦1 and u+v+w=1; forming, in an upper portion of the first nitride semiconductor layer, plural convexes extending at intervals along a substrate surface direction; forming a mask for covering bottoms and at least part of walls of recesses formed between the convexes adjacent to each other; and forming, on the first nitride semiconductor layer, a second nitride semiconductor layer of Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1, by using, as a seed crystal, portions of the convexes exposed from the mask film. 
     In the second method of fabricating a nitride semiconductor, even when polycrystals of the second nitride semiconductor layer are deposited on the mask film in growing the second nitride semiconductor layer in a direction parallel to the substrate surface, the second nitride semiconductor layer grows over the polycrystals owing to the mask film formed on the bottoms and at least part of the walls of the recesses between the convexes. Accordingly, the second nitride semiconductor layer is never prevented from growing by the polycrystals, resulting in attaining good crystallinity. 
     The first method of fabricating a nitride semiconductor device of this invention achieves the first object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms of the grooves; growing, by using, as a seed crystal, C planes corresponding to portions of a top face of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; and forming, on the lamination body, a current confinement part for selectively injecting carriers into the active layer. 
     In the first method of fabricating a nitride semiconductor device, the lamination body including the active layer is formed by the first method of fabricating a nitride semiconductor of this invention. Accordingly, the active layer and the nitride semiconductor layers sandwiching the active layer in the vertical direction attain good crystallinity. As a result, there liability of the semiconductor device can be largely improved. 
     The second method of fabricating a nitride semiconductor device of this invention achieves the first object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms and at least part of walls of the grooves; growing, by using, as a seed crystal, portions of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; and forming, on the lamination body, a current confinement part for selectively injecting carriers into the active layer. 
     In the second method of fabricating a nitride semiconductor device, the lamination body including the active layer is formed by the second method of fabricating a nitride semiconductor of this invention. Accordingly, the active layer and the nitride semiconductor layers sandwiching the active layer in the vertical direction attain good crystallinity. As a result, the reliability of the semiconductor device can be largely improved. 
     The third method of fabricating a nitride semiconductor of this invention achieves the first object and comprises the steps of forming, in an upper portion of a substrate, plural convexes extending at intervals along a substrate surface direction; and selectively growing a nitride semiconductor layer of Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1, on top faces of the convexes of the substrate. 
     In the third method of fabricating a nitride semiconductor, not only the same effect as that of the first method of fabricating a nitride semiconductor can be attained but also there is no need to form a semiconductor layer as a seed crystal because the convexes in the shape of stripes are formed in the substrate itself. Furthermore, when the substrate is not a nitride semiconductor, there is no need to provide a mask film for selective growth, resulting in largely simplifying the fabrication process of the semiconductor. 
     The third method of fabricating a nitride semiconductor device of this invention achieves the first object and comprises the steps of forming, in an upper portion of a substrate, plural grooves extending at intervals along a substrate surface direction; selectively growing, on a top face of the substrate between the grooves, a lamination body including a first nitride semiconductor layer, an active layer formed from a second nitride semiconductor layer having a smaller energy gap than the first nitride semiconductor layer and a third nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; and forming, on the lamination body, a current confinement part f or selectively injecting carriers into the active layer. 
     In the third method of fabricating a nitride semiconductor device, the lamination body including the active layer is formed by the third method of fabricating a nitride semiconductor of this invention. Accordingly, the active layer and the nitride semiconductor layers sandwiching the active layer in the vertical direction attain good crystallinity and the fabrication process can be largely simplified, resulting in improving the productivity. 
     The first nitride semiconductor device of this invention achieves the second object and comprises a lamination body including a first nitride semiconductor layer, an active layer formed from a second nitride semiconductor layer having a larger refractive index than the first nitride semiconductor layer and a third nitride semiconductor layer having a smaller refractive index than the active layer successively stacked on a substrate; and a current confinement part formed on the lamination body for selectively injecting carriers into the active layer, and a gap is formed in a region below the current confinement part and between the active layer and the substrate. 
     In the first nitride semiconductor device, the gap with a smaller refractive index than the semiconductor is formed in the region below the current confinement part and between the active layer and the substrate. Accordingly, light generated in the active layer is less leaked to the substrate, resulting in increasing the confinement coefficient of the generated light in the active layer. 
     The second nitride semiconductor device of this invention achieves the second object and comprises a first nitride semiconductor layer formed on a substrate and including, in an upper portion thereof, plural convexes extending at intervals along a substrate surface direction; a second nitride semiconductor layer formed on the first nitride semiconductor layer with a lower face thereof in contact with top faces of the convexes; and a lamination body formed on the second nitride semiconductor layer and including a third nitride semiconductor layer, an active layer formed from a fourth nitride semiconductor layer having a larger refractive index than the third nitride semiconductor layer and a fifth nitride semiconductor layer having a smaller refractive index than the active layer, and the second nitride semiconductor layer has a refractive index smaller than or equivalent to a refractive index of the third nitride semiconductor layer. 
     In the second nitride semiconductor device, the second nitride semiconductor layer is grown by using, as the seed crystal, the top faces of the convexes formed in the shape of stripes in the upper portion of the first nitride semiconductor layer. Accordingly, gaps are formed between the convexes of the first nitride semiconductor layer below the second nitride semiconductor layer. Furthermore, the second nitride semiconductor layer has a refractive index smaller than or equivalent to that of the third nitride semiconductor layer, the light confinement coefficient in the active layer can be definitely increased by providing a current confinement part in the lamination body above the gap. 
     The fourth method of fabricating a nitride semiconductor device of this invention achieves the second object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms of the grooves; growing, by using, as a seed crystal, C planes corresponding to portions of a top face of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, a third nitride semiconductor layer, an active layer formed from a fourth nitride semiconductor layer having a larger refractive index than the third nitride semiconductor layer and a fifth nitride semiconductor layer having a smaller refractive index than the active layer stacked in this order from a substrate side; and forming, on the lamination body, a current confinement part for selectively injecting carriers into the active layer, and the step of growing the lamination body includes a sub-step of growing the second nitride semiconductor layer with a refractive index thereof smaller than or equivalent to a refractive index of the third nitride semiconductor layer. 
     According to the fourth method of fabricating a nitride semiconductor device, the second nitride semiconductor device of the invention can be definitely fabricated. 
     The fifth method of fabricating a nitride semiconductor device of this invention achieves the second object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms and at least part of walls of the grooves; growing, by using, as a seed crystal, portions of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, a third nitride semiconductor layer, an active layer formed from a fourth nitride semiconductor layer having a larger refractive index than the third nitride semiconductor layer and a fifth nitride semiconductor layer having a smaller refractive index than the active layer stacked in this order from a substrate side; and forming, on the lamination body, a current confinement part for selectively injecting carriers into the active layer, and the step of growing the lamination body includes a sub-step of growing the second nitride semiconductor layer with a refractive index thereof smaller than or equivalent to a refractive index of the third nitride semiconductor layer. 
     According to the fifth method of fabricating a nitride semiconductor device, the second nitride semiconductor device of the invention can be definitely fabricated. 
     The fourth method of fabricating a nitride semiconductor of this invention achieves the third object and comprises the steps of forming, on a substrate, a first nitride semiconductor layer of Al u Ga v In w N, wherein 0≦u, v, w≦1 and u+v+w=1; forming, in an upper portion of the first nitride semiconductor layer, plural convexes extending at intervals along a substrate surface direction; forming a mask film for covering bottoms of recesses formed between the convexes adjacent to each other; and growing, on the first nitride semiconductor layer, plural second nitride semiconductor layers of Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1, by using, as a seed crystal, C planes corresponding to top faces of the convexes exposed from the mask film, and the step of forming the plural second nitride semiconductor layers includes a sub-step of forming each of the second nitride semiconductor layers in a manner that a facet of the second nitride semiconductor layer parallel to a direction of extending the convexes is exposed every time the second nitride semiconductor layer extends over a given number of convexes among the plural convexes. 
     In the fourth method of fabricating a nitride semiconductor, each of the second nitride semiconductor layers is formed so as to expose the facet parallel to the direction of extending the convexes every time the second nitride semiconductor layer extends over a given number of convexes among the plural convexes formed in the upper portion of the first nitride semiconductor layer. Accordingly, when the facet is used as a cavity facet, the cavity facet is obtained without being affected by a cleaved end and an etched end, resulting in reducing mirror loss of the cavity facet. 
     The fifth method of fabricating a nitride semiconductor of this invention achieves the third object and comprises the steps of forming, on a substrate, a first nitride semiconductor layer of Al u Ga v In w N, wherein 0≦u, v, w≦1 and u+v+w=1; forming, in an upper portion of the first nitride semiconductor layer, plural convexes extending at intervals along a substrate surface direction; forming a mask film for covering bottoms and at least part of walls of recesses formed between the convexes adjacent to each other; and forming, on the first nitride semiconductor layer, plural second nitride semiconductor layers of Al x Ga y In z N, wherein 0≦x, y, z≦1 and x+y+z=1, by using, as a seed crystal, portions of the convexes exposed from the mask film, and the step of forming the plural second nitride semiconductor layers includes a sub-step of forming each of the second nitride semiconductor layers in a manner that a facet of the second nitride semiconductor layer parallel to a direction of extending the convexes is exposed every time the second nitride semiconductor layer extends over a given number of convexes among the plural convexes. 
     In the fifth method of fabricating a nitride semiconductor, each of the second nitride semiconductor layers is formed so as to expose the facet parallel to the direction of extending the convexes every time the second nitride semiconductor layer extends over a given number of convexes among the plural convexes formed in the upper portion of the first nitride semiconductor layer. Accordingly, when the facet is used as a cavity facet, the cavity facet is obtained without being affected by a cleaved end or an etched end, resulting in reducing mirror loss of the cavity facet. 
     The sixth method of fabricating a nitride semiconductor device of this invention achieves the third object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms of the grooves; growing, by using, as a seed crystal, C planes corresponding to portions of a top face of the first nitride semiconductor layer exposed from the mask film between the grooves, plural lamination bodies each including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; and forming, on each of the lamination bodies, a current confinement part for selectively injecting carriers into the active layer, and the step of growing the plural lamination bodies includes a sub-step of forming each of the lamination bodies in a manner than a cavity facet including the current confinement part is exposed every time the lamination body extends over a given number of C planes of the first nitride semiconductor layer. 
     In the sixth method of fabricating a nitride semiconductor device, the lamination bodies each including the active layer are formed by the fourth method of fabricating a nitride semiconductor of this invention. Accordingly, the cavity facet is obtained without being affected by a cleaved end or an etched end, resulting in reducing mirror loss of the cavity facet. 
     The seventh method of fabricating a nitride semiconductor device of this invention achieves the third object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals along a substrate surface direction; forming a mask film for covering bottoms and at least part of walls of the grooves; growing, by using, as a seed crystal, portions of the first nitride semiconductor layer exposed from the mask film between the grooves, plural lamination bodies each including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; and forming, on each of the lamination bodies, a current confinement part for selectively injecting carriers into the active layer, and the step of growing the plural lamination bodies includes a sub-step of forming each of the lamination bodies in a manner than a cavity facet including the current confinement part is exposed every time the lamination body extends over a given number of portions of the first nitride semiconductor layer sandwiched between the grooves adjacent to each other. 
     In the seventh method of fabricating a nitride semiconductor device, the lamination bodies each including the active layer are formed by the fifth method of fabricating a nitride semiconductor of this invention. Accordingly, the cavity facet is obtained without being affected by a cleaved end or an etched end, resulting in reducing mirror loss of the cavity facet. 
     The third nitride semiconductor device of this invention achieves the third and fourth objects and comprises a first nitride semiconductor layer formed on a substrate and including, in an upper portion thereof, plural convexes extending at intervals along a substrate surface direction; a second nitride semiconductor layer formed on the first nitride semiconductor layer with gaps formed between side faces of the convexes; and a third nitride semiconductor layer formed on the second nitride semiconductor layer and including a cavity in the shape of a stripe into which confined carriers are injected, and the cavity is provided with a resonating direction of generated light substantially perpendicular to a direction of extending the convexes. 
     In the third nitride semiconductor device, the cavity is provided so that the resonating direction of generated light can be substantially perpendicular to the direction of extending the convexes. Therefore, when the direction of extending the convexes is, for example, the M-axis direction and the resonating direction of the cavity is the A-axis direction, the cavity facet accords with the A plane. Accordingly, when the substrate is formed from sapphire, the cleaved end of the substrate is the M plane, and hence, the cleave can be eased so as to improve the yield in the cleavage. Also, in this case, although the cavity crosses plural convexes working as the seed crystal, the waveguide loss is also reduced because the tilt in the C-axis between the first nitride semiconductor layer and the second nitride semiconductor layer is suppressed by the gaps formed in the first nitride semiconductor layer between the side faces of the convexes. 
     The eighth method of fabricating a nitride semiconductor device of this invention achieves the third and fourth objects and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural first grooves extending at intervals along one substrate surface direction; forming a first mask film for covering bottoms of the first grooves; growing a second nitride semiconductor layer by using, as a seed crystal, C planes corresponding to portions of a top face of the first nitride semiconductor layer exposed from the first mask film between the first grooves; forming, in an upper portion of the second nitride semiconductor layer, plural second grooves extending at intervals in the one substrate surface direction and having portions between the second grooves adjacent to each other in different positions, in a substrate surface direction, from the portions between the first grooves adjacent to each other; forming a second mask film for covering bottoms of the second grooves; growing a third nitride semiconductor layer including an active layer by using, as a seed crystal, C planes corresponding to portions of a top face of the second nitride semiconductor layer exposed from the second mask film between the second grooves; and forming, on the third nitride semiconductor layer, a current confinement part with a resonating direction of generated light substantially perpendicular to the one substrate surface direction. 
     According to the eighth method of fabricating a nitride semiconductor device, the third nitride semiconductor device of the invention can be definitely fabricated. 
     The ninth method of fabricating a nitride semiconductor device of this invention achieves the third and fourth objects and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural first grooves extending at intervals along one substrate surface direction; forming a first mask film for covering bottoms and at least part of walls of the first grooves; growing a second nitride semiconductor layer by using, as a seed crystal, portions of the first nitride semiconductor layer exposed from the first mask film between the first grooves; forming, in an upper portion of the second nitride semiconductor layer, plural second grooves extending at intervals along the one substrate surface direction and having portions between the second grooves adjacent to each other in positions different, in a substrate surface direction, from portions between the first grooves adjacent to each other; forming a second mask film for covering bottoms and at least part of walls of the second grooves; growing a third nitride semiconductor layer including an active layer by using, as a seed crystal, portions of the second nitride semiconductor layer exposed from the second mask film between the second grooves; and forming, on the third nitride semiconductor layer, a current confinement part with a resonating direction of generated light substantially perpendicular to the one substrate surface direction. 
     According to the ninth method of fabricating a nitride semiconductor device, the third nitride semiconductor device of the invention can be definitely fabricated. 
     The semiconductor light emitting device of this invention achieves the fifth object and comprises a first semiconductor layer formed on a substrate and including, in an upper portion thereof, plural first convexes extending at intervals along a substrate surface direction; and a second semiconductor layer formed from a lamination body including an active layer on the first semiconductor layer in contact with the first convexes and including, in an upper portion thereof, plural second convexes extending in a direction the same as the first convexes at intervals different from the intervals of the first convexes, and carriers are injected into the active layer from a top face of one of the plural second convexes. 
     The second semiconductor layer generally formed by the ELOG includes a large number of threading dislocations in regions above the first convexes, and hence, it is necessary to form a current injecting region in a position excluding such regions. In the semiconductor light emitting device of this invention, since there is a difference between the formation cycle of the first convexes and the formation cycle of the second convexes, there appears, on the substrate, a region where the first convex accords with the second convex in a cycle larger than the formation cycles of these convexes. An alignment mark can be easily and definitely provided by using this large cycle, resulting in improving the yield and the throughput of the fabrication process. 
     The first method of fabricating a semiconductor light emitting device of this invention achieves the fifth object and comprises the steps of forming a first semiconductor layer on a substrate and forming, in an upper portion of the first semiconductor layer, plural first convexes extending at intervals along a substrate surface direction; forming, on the first semiconductor layer, a second semiconductor layer having a lower face in contact with the first convexes from a lamination body including an active layer, and forming, in an upper portion of the second semiconductor layer, plural second convexes extending in a direction the same as the first convexes at intervals different from the intervals of the first convexes; forming, on the substrate, a mark for aligning a mask for identifying a convex for injecting carriers into the active layer among the plural second convexes; and aligning the mask by using the mark and forming one of the plural second convexes into a carrier injection part by using the mask. 
     According to the first method of fabricating a semiconductor light emitting device, the semiconductor light emitting device of this invention can be definitely fabricated. 
     The second method of fabricating a semiconductor light emitting device of this invention achieves the fifth object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals in a substrate surface direction; forming a mask film for covering bottoms of the grooves; growing, by using, as a seed crystal, C planes corresponding to portions of a top face of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; forming, in an upper portion of the lamination body, plural convexes extending in a direction the same as the grooves at intervals different from the intervals of the grooves; and selecting one convex in a position above any of the grooves and in the vicinity of an area between the grooves among the plural convexes and forming the selected convex into a carrier injection part for injecting carriers into the active layer. 
     According to the second method of fabricating a semiconductor light emitting device, the semiconductor light emitting device of this invention can be definitely fabricated. 
     The third method of fabricating a semiconductor light emitting device of this invention achieves the fifth object and comprises the steps of forming a first nitride semiconductor layer on a substrate; forming, in an upper portion of the first nitride semiconductor layer, plural grooves extending at intervals in a substrate surface direction; forming a mask film for covering bottoms and at least part of walls of the grooves; growing, by using, as a seed crystal, portions of the first nitride semiconductor layer exposed from the mask film between the grooves, a lamination body including a second nitride semiconductor layer, an active layer formed from a third nitride semiconductor layer having a smaller energy gap than the second nitride semiconductor layer and a fourth nitride semiconductor layer having a larger energy gap than the active layer stacked in this order from a substrate side; forming, in an upper portion of the lamination body, plural convexes extending in a direction the same as the grooves at intervals different from the intervals of the grooves; and selecting one convex in a position above any of the grooves and in the vicinity of an area between the grooves among the plural convexes and forming the selected convex into a carrier injection part for injecting carriers into the active layer. 
     According to the third method of fabricating a semiconductor light emitting device, the semiconductor light emitting device of this invention can be definitely fabricated. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 1 of the invention; 
       FIGS.  2 ( a ) and  2 ( b ) are cross-sectional views for showing procedures in fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 1; 
       FIGS.  3 ( a ) and  3 ( b ) are cross-sectional views for showing other procedures in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 1; 
         FIG. 4  is a cross-sectional view for showing another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 1: 
         FIG. 5  is a schematic cross-sectional view for showing the characteristic of the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 1; 
       FIGS.  6 ( a ),  6 ( b ),  6 ( c ) and  6 ( d ) are schematic cross-sectional views for showing, in a stepwise manner, the characteristic of the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 1; 
         FIG. 7  is a graph for showing comparison in photoluminescence at room temperature of a selectively grown layer between a gallium nitride-based semiconductor laser diode according to Modification 1 of Embodiment 1 and the semiconductor laser diode of Embodiment 1; 
         FIG. 8  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Modification 2 of Embodiment 1; 
         FIG. 9  is across-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 2 of the invention; 
       FIGS.  10 ( a ) and  10 ( b ) are cross-sectional views for showing procedures in fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 2; 
         FIG. 11  is a cross-sectional view for showing another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 2; 
         FIG. 12  is across-sectional view for showing still another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 2; 
         FIG. 13  is a graph for showing a far-field pattern, along a direction parallel to a cavity facet, of a laser beam emitted from the gallium nitride-based semiconductor laser diode of Embodiment 2; 
         FIG. 14  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 3 of the invention; 
         FIG. 15  is a graph for showing the relationship between the distribution of a refractive index in a ridge along a direction vertical to a substrate surface and the distribution of light intensity on a cavity facet in the gallium nitride-based semiconductor laser diode of Embodiment 3; 
         FIG. 16  is a graph for showing a far-field pattern, along a direction parallel to the cavity facet, of a laser beam emitted by the gallium nitride-based semiconductor laser diode of Embodiment 3; 
         FIG. 17  is a plane photograph obtained with an optical microscope and a corresponding cross-sectional view of a selectively grown layer before forming a lamination body  30  in the gallium nitride-based semiconductor laser diode of Embodiment 3; 
         FIG. 18  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 4 of the invention; 
       FIG.  19 ( a ) is a cross-sectional view for schematically showing a selective growth mechanism in fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 4; 
       FIG.  19 ( b ) is a cross-sectional view for schematically showing a selective growth mechanism in fabrication of a gallium nitride-based semiconductor laser diode according to Conventional Example 2; 
       FIG.  20 ( a ) is a partial perspective view for showing an effect of forming a selectively grown layer in two steps in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 4; 
       FIG.  20 ( b ) is a partial perspective view for comparison for showing a state where roughness is caused on a side face of a selectively grown layer of a gallium nitride-based semiconductor laser diode; 
       FIGS.  21 ( a ),  21 ( b ),  21 ( c ) and  21 ( d ) are schematic cross-sectional views for showing, in a stepwise manner, the characteristic of the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 4; 
         FIG. 22  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 5 taken on the M plane of a lamination body, namely, the A plane of a substrate; 
         FIG. 23  is a cross-sectional view of the gallium nitride-based semiconductor laser diode of Embodiment 5 taken on line XXIII—XXIII of  FIG. 22 ; 
         FIG. 24  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Modification 1 of Embodiment 5 taken on the M plane of a lamination body, namely, the A plane of a substrate; 
         FIG. 25  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Modification 2 of Embodiment 5 taken on the M plane of a lamination body, namely, the A plane of a substrate; 
         FIG. 26  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Modification 3 of Embodiment 5 taken on the M plane of a lamination body, namely, the A plane of a substrate; 
         FIG. 27  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 6 of the invention taken on the A plane of a lamination body, namely, the M plane of a substrate; 
       FIGS.  28 ( a ) and  28 ( b ) are cross-sectional views for showing procedures in fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 6; 
       FIGS.  29 ( a ) and  29 ( b ) are cross-sectional views for showing other procedures in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 6; 
       FIGS.  30 ( a ) and  30 ( b ) are cross-sectional views for showing still other procedures in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 6; 
         FIG. 31  is a cross-sectional view for showing another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 6; 
         FIG. 32  is a cross-sectional view for showing the structure of a gallium nitride-based semiconductor laser diode according to Embodiment 7 of the invention; 
         FIG. 33  is a cross-sectional view for showing a procedure in fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 7; 
         FIG. 34  is a cross-sectional view for showing another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 7; 
         FIG. 35  is across-sectional view for showing still another procedure in the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 7; 
       FIGS.  36 ( a ) and  36 ( b ) show the fabrication of the gallium nitride-based semiconductor laser diode of Embodiment 7, wherein FIG.  36 ( a ) is a cross-sectional view of an appropriate ridge and an inappropriate ridge for use in current injection and FIG.  36 ( b ) is a cross-sectional view of a state where identification marks are cyclically provided on respective ridges; 
         FIG. 37  is a cross-sectional view of a gallium nitride-based semiconductor laser diode according to Conventional Example 1; 
         FIG. 38  is across-sectional view for schematically showing the distribution of crystal dislocations in gallium nitride formed by ELOG according to Conventional Example 2; 
         FIG. 39  is a cross-sectional view for showing the structure of the gallium nitride-based semiconductor laser diode of Conventional Example 2; 
       FIGS.  40 ( a ),  40 ( b ),  40 ( c ) and  40 ( d ) are schematic cross-sectional views for showing, in a stepwise manner, crystal growth in fabrication of the gallium nitride-based semiconductor laser diode of Conventional Example 2; 
         FIG. 41  is a graph for showing the relationship, in the gallium nitride-based semiconductor laser diode of Conventional Example 1, the distribution of a refractive index, along a direction vertical to a substrate surface, in a ridge and the distribution of light intensity on a cavity facet; 
         FIG. 42  is a graph for showing a far-field pattern of the gallium nitride-based semiconductor laser diode of Conventional Example 1; and 
         FIG. 43  is a schematic perspective view of cleaved ends of a substrate and a cavity in the gallium nitride-based semiconductor laser diode of Conventional Example 1. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiment 1 
     Embodiment 1 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 1  shows the sectional structure of a gallium nitride-based semiconductor laser diode according to this embodiment. 
     As is shown in  FIG. 1 , on a substrate  11  of sapphire (crystalline Al 2 O 3 ), a seed layer  12  of gallium nitride (GaN) for ELOG is formed with a low temperature buffer layer (not shown) of GaN sandwiched therebetween. 
     Convexes  12   a  in the shape of stripes extending at intervals along a substrate surface direction are formed in an upper portion of the seed layer  12 , and a mask film  13  of silicon nitride (SiN x ) is formed on the bottom and the walls of each concave (groove)  12   b  formed between the convexes  12   a.    
     On the seed layer  12 , a selectively grown layer  14  of GaN is formed so as to be in contact with the respective convexes  12   a  and to have gaps  12   c  between its lower face and the bottoms of the grooves  12   b.    
     The group III elements of the seed layer  12  and the selectively grown layer  14  are not limited to gallium but may include aluminum and indium. Specifically, the materials for the seed layer  12  and the selectively grown layer  14  are represented by Al u Ga v In w N, wherein 0≦u, v, w≦1 and u+v+w=1. 
     On the selectively grown layer  14 , a lamination body  30  consisting of plural nitride semiconductor layers including double heterojunction of the laser diode is formed. 
     Specifically, the lamination body  30  includes an n-type contact layer  15  of n-type GaN, an n-type cladding layer  16  of n-type Al 0.07 Ga 0.93 N, an n-type light guiding layer  17  of n-type GaN, a multiple quantum well (MQW) active layer  18  including a well layer of Ga 0.8 In 0.2 N with a thickness of approximately 3 nm and a barrier layer of GaN with a thickness of 6 nm, a p-type light guiding layer  19  of p-type GaN, a p-type cladding layer  20  of p-type Al 0.07 Ga 0.93 N and a p-type contact layer  21  of p-type GaN successively formed on the selectively grown layer  14 . 
     As is well known, in the double heterojunction type laser structure, the energy gap of the well layer containing indium and included in the MQW active layer  18  is smaller than the energy gap of the n-type and p-type cladding layers  16  and  20  containing aluminum. On the other hand, the refractive index is the largest in the well layer of the MQW active layer  18  and is smaller in the order of the light guiding layers  17  and  19  and the cladding layers  16  and  20 . 
     An upper portion of the p-type cladding layer  20  and the p-type contact layer  21  is formed into a ridge  31  working as a current confining portion corresponding to a current injecting region with a width of approximately 3 through 5 μm. 
     The lamination body  30  including the MQW active layer  18  is etched so as to partly expose the n-type contact layer  15 , and the top face and the side face of the etched lamination body  30  are covered with an insulating film  22  of silicon oxide. 
     In a portion of the insulating film  22  on the p-type contact layer  21 , an opening parallel to the convex  12   a  is formed. On a portion of the insulating film  22  over and on both sides of the ridge  31 , a p-side electrode  23  including stacked layers of nickel (Ni) and gold (Au) is formed to be in ohmic contact with the p-type contact layer  21  through the opening. 
     On a portion of the n-type contact layer  15  not covered with the insulating film  22 , an n-side electrode  24  including stacked layers of titanium (Ti) and aluminum (Al) is formed so as to be in ohmic contact with the n-type contact layer  15 . 
     At this point, the ridge  31  is formed in a dislocation low-density region including fewer crystal dislocations positioned above the gap  12   c.    
     Now, a method of fabricating the semiconductor laser diode having the aforementioned structure will be described with reference to the accompanying drawings. 
     FIGS.  2 ( a ),  2 ( b ),  3 ( a ),  3 ( b ) and  4  are sectional views for showing procedures in the method of fabricating the semiconductor laser diode of Embodiment 1. 
     First, as is shown in FIG.  2 ( a ), after setting the substrate temperature at approximately 500° C. through 530° C., trimethyl gallium (TMG) serving as a group III element source and ammonia (NH 3 ) serving as a nitrogen source are supplied onto a substrate  11  having the C plane (=the (0001) surface orientation) as the principal plane by, for example, MOVPE, thereby depositing a low temperature buffer layer (not shown) of GaN. Subsequently, after increasing the substrate temperature to approximately 1020° C. through 1030° C., TMG and NH 3  are supplied onto the substrate  11 , thereby growing a seed layer  12  of GaN. 
     Next, as is shown in FIG.  2 ( b ), after applying a resist film on the seed layer  12 , the resist film is patterned into stripes by photolithography, thereby forming a resist pattern  40 . Then, the seed layer  12  is dry etched by using the resist pattern  40  as a mask. Thus, a cyclic structure including, as one cycle, a convex  12   a  with a sectional width of approximately 3 μm and a groove (recess)  12   b  with a sectional width of approximately 12 μm is formed in the upper portion of the seed layer  12 . 
     Then, as is shown in FIG.  3 ( a ), a mask film  13  of silicon nitride is deposited on the bottoms and the walls of the grooves  12   b  of the seed layer  12  and the resist pattern  40  by electron cyclotron resonance (ECR) sputtering. At this point, solid silicon is used as the raw material of silicon, nitrogen is used as a reaction gas and argon is used as plasma gas. Since the ECR sputtering is employed for depositing the mask film  13 , the mask film  13  with high quality can be formed at a low temperature. 
     Next, as is shown in FIG.  3 ( b ), the resist pattern  40  is lifted off, thereby removing the resist pattern  40  and a portion of the mask film  13  deposited on the resist pattern  40 . The mask film  13  may cover whole or a part of the wall of the groove  12   b.    
     Subsequently, as is shown in  FIG. 4 , a selectively grown layer  14  of GaN is grown on the seed layer  12  by the MOVPE again by using, as the seed crystal, the C plane appearing on the top faces of the convexes  12   a  exposed from the mask film  13 . At this point, the selectively grown layer  14  grows upward from the top face of each convex  12   a  as well as grows along a direction parallel to the substrate surface (i.e., laterally grows). Therefore, the crystals grown from the both sides of each groove  12   b  meet each other at substantially the center of the groove  12   b , so as to form a junction portion  14   a . As a result, the respective crystals grown from the top faces of the plural convexes  12   a  are integrated and the integrated top face accords with the C plane. Subsequently, on the integrated selectively grown layer  14 , an n-type contact layer  15 , an n-type cladding layer  16 , an n-type light guiding layer  17 , a MQW active layer  18 , a p-type light guiding layer  19 , a p-type cladding layer  20  and a p-type contact layer  21  are successively grown, thereby forming a lamination body  30 . 
     Thereafter, as is shown in  FIG. 1 , a ridge  31  for selectively injecting a current into the MWQ active layer  18  is formed from the upper portion of the p-type cladding layer  20  and the p-type contact layer  21  in a dislocation low-density region positioned above the gap  12   c  and not overlapping the junction portion  14   a.    
     Then, the lamination body  30  excluding the ridge  31  is dry etched so as to partly expose the n-type contact layer  15 , and an insulating film  22  is deposited on the exposed faces of the lamination body  30 . Next, after selectively forming openings in portions of the insulating film  22  on the ridge  31  and the n-type contact layer  15 , a p-side electrode  23  is formed over and on both sides of the ridge  31  exposed in the opening of the insulating film  22  and an n-side electrode  24  is formed on a portion of the n-type contact layer  15  exposed in the opening of the insulating film  22  by deposition or sputtering. 
     In the semiconductor laser diode thus fabricated, when a predetermined voltage in a forward direction is applied between the p-side electrode  23  and the n-side electrode  24 , holes are injected from the p-side electrode  23  and electrons are injected from the n-side electrode  24  into the MQW active layer  18 . As a result, optical gain is generated in the MQW active layer  18 , so as to show laser action at a wavelength of approximately 404 nm. 
     As is shown in  FIG. 5 , in a portion of the selectively grown layer  14  above the seed crystal, namely, above the convex  12   a , a dislocation high-density region  14   b  with a dislocation density of approximately 1×10 9  cm −2  is formed. On the other hand, a laterally grown region of the selectively grown layer  14  is formed into a dislocation low-density region  14   c  with a dislocation density of approximately 1×10 7  cm −2 . Accordingly, when the ridge  31 , namely, the current injecting region serving as a cavity of laser, is formed above the dislocation low-density region  14   c  of the lamination body  30 , the reliability of the laser diode can be improved. 
     Now, the effect attained by the grooves  12   b  of the seed layer  12 , that is, the characteristic of this embodiment, will be described with reference to FIGS.  6 ( a ) through  6 ( d ). 
     As is shown in FIG.  6 ( a ), the grooves  12   b  in the shape of stripes are formed in the upper portion of the seed layer  12 , and the mask film  13  is formed at least on the bottoms of the grooves. 
     Then, as is shown in FIGS.  6 ( b ) and  6 ( c ), the selectively grown layers  14  are grown by using, as the seed crystal, the top faces of the convexes  12   a  sandwiched between the grooves  12   b . At this point, polycrystals  41  of GaN may be deposited on the mask film  13 . 
     Next, as is shown in FIG.  6 ( d ), even when the selectively grown layers  14  are integrated by continuing the ELOG with the polycrystals  41  deposited, there still remains a level difference between the top face of the convex  12   a  serving as the seed crystal and the bottom of the groove  12   b  where the polycrystal  41  is deposited Accordingly, the polycrystals  41  never affect the crystallinity of the selectively grown layer  14  and the lamination body  30 . As a result, variation in the crystallinity of the lamination body  30  can be largely reduced, so as to largely improve the yield in the fabrication of the semiconductor laser diode. 
     The junction portion  14   a  threading the selectively grown layer  14  and the lamination body  30  shown in  FIG. 1  along a direction vertical to the substrate surface is formed as a small angle boundary where edge dislocations are collected. Accordingly, although electrons injected from the n-side electrode  24  pass through a plurality of junction portions  14   a  to reach the MQW active layer  18 , the dislocations collected in the junction portions  14   a  never prevent the injection of the electrons. 
     In forming the semiconductor laser diode on a chip, it is necessary to form a cavity facet working as a mirror face of the cavity. In general, the cavity facet of a semiconductor laser diode is formed by cleaving the substrate  11 , and flaws and cracks may be caused in the substrate  11  during the cleavage. 
     In the fabrication method for a semiconductor laser diode of Conventional Example 2 shown in  FIG. 39 , since the substrate  401  and the lowermost semiconductor layer  404  are in contact with each other, a flaw caused in the substrate  401  may reach the lamination body including the MQW active layer  306 , which can disadvantageously largely spoil the operation and the optical characteristics of the laser diode. 
     On the other hand, according to this embodiment, since the gaps  12   c  are provided between the substrate  11  and the lamination body  30 , flaws caused in the substrate  11  can be stopped by the gaps  12   c . Accordingly, possibility of damage of the lamination body  30  due to the flaws caused in the substrate  11  can be remarkably reduced. 
     Furthermore, in the fabrication method for a semiconductor laser diode of Conventional Example 1 shown in  FIG. 37 , when a nitride semiconductor layer is grown on the substrate  301  of sapphire or silicon carbide, the dislocation density of the crystal is as high as approximately 10 9  cm −2 . In the semiconductor crystal having such a high dislocation density, a step on the crystal surface is terminated during step flow growth due to the dislocations, screw dislocations in particular, included at a high density, resulting in forming microfacets on the crystal surface. Accordingly, the crystal surface becomes irregular and the crystal becomes poor in flatness. As a result, in growing the MQW active layer  306  including indium, the quantity of a raw material of indium incorporated into the crystal is varied, resulting in causing harmful effects such as increase of the threshold current of the laser diode. 
     In the fabrication method of this embodiment, uniform step flow growth is observed in a laterally grown region, namely, the dislocation low-density region  14   c  of  FIG. 5 , and the crystal surface is good at flatness. As a result, in growing the MQW active layer  18 , local segregation of indium can be avoided, resulting in lowering the threshold current. 
     The MOVPE is used for growing the nitride semiconductor in this embodiment, which does not limit the invention. Any growth method other than the MOVPE such as halide vapor phase epitaxial (HVPE) growth and molecular beam epitaxial (MBE) growth may be used as far as a nitride semiconductor can be grown. This goes for respective embodiments described below. 
     Furthermore, although the substrate  11  is made from sapphire in this embodiment, for example, silicon carbide, neodymium gallate (NGO), gallium nitride or the like can be used instead of sapphire. 
     Although the seed layer  12  is grown on the substrate  11  in two steps with the low temperature buffer layer formed therebetween in this embodiment, the low temperature buffer layer is not always necessary as far as the seed layer  12  can be formed in monocrystal. 
     Although the lift-off method is employed for forming the convexes  12   a  in the upper portion of the seed layer  12  in this embodiment, any other method can be employed as far as the convexes  12   a  and the grooves  12   b  can be formed with the mask film  13  remaining at least on the bottoms of the grooves  12   b . In other words, any method can be employed as far as the C plane of the convexes  12   a  not covered with the mask film  13  can be used as the seed crystal and the gaps  12   c  can be formed. Furthermore, in stead of forming the convexes  12   a  through recess etching for etching the upper portion of the seed layer  12 , a mask film for selective growth with an opening pattern in the shape of stripes may be formed on the flat top face of the seed layer  12  so as to grow the convexes projecting from the opening pattern of the mask film. 
     Moreover, the mask film  13  may be formed merely on the bottoms of the grooves  12   b  as far as the gaps  12   c  can be formed. 
     Although the mask film  13  is formed from silicon nitride in this embodiment, another dielectric film or a amorphous insulating film may be used instead of the silicon nitride film. Specifically, silicon oxide (SiO 2 ), nitrided silicon oxide (SiON), aluminum oxide (Al 2 O 3 ), nitrided aluminum oxide (AlNO), titanium oxide (TiO 2 ), zirconium oxide (ZrO 2 ) or niobium oxide (Nb 2 O 3 ) may be used. Films of these materials can be comparatively easily formed by the ECR sputtering. 
     Modification 1 of Embodiment 1 
     As Modification 1 of Embodiment 1, a mask film of a metal with a high melting point or a metal compound with a high melting point will be described. 
     When tungsten (W), that is, a metal with a high melting point, is used for the mask film  13  for the selective growth, the selectivity of crystal growth can be improved as compared with the case where the mask film  13  is formed from a dielectric, and hence, deposition of polycrystals  41  on the mask film  13  can be further suppressed. As a result, the lamination body  30  with high quality can be very easily formed without being affected by the polycrystals  41 . 
     This is because the bonding strength between the mask film  13  and the nitride semiconductor crystal is lower when the mask film  13  is formed from a metal than when it is formed from a dielectric. 
     Tungsten, that is, a metal with a high melting point, is stable in its characteristics owing to its melting point of 3380° C. the highest among those of metals and its low vapor pressure. Therefore, an impurity such as silicon and oxygen can be prevented from being mixed in the selectively grown layer  14  differently from the case where a dielectric such as silicon oxide is used. As a result, a deep level and a non-luminescent center are never formed in the selectively grown layer  14  formed by using the mask film  13  of tungsten. 
       FIG. 7  shows comparison in photoluminescence at room temperature between a selectively grown layer  14  formed by using a mask film  13  of a dielectric and a selectively grown layer  14  formed by using a mask film  13  of a metal with a high melting point. 
     As is shown in  FIG. 7 , in the selectively grown layer  14  of Modification 1, there is no luminescence at a deep level of a wavelength of approximately 430 nm, and very strong luminescence can be obtained at the end of the band. This reveals that the selectively grown layer  14  of Modification 1 has higher quality than the selectively grown layer  14  of Embodiment 1. Accordingly, when the lamination body  30  is grown on the selectively grown layer  14  with such high quality, the MQW active layer  18  can attain higher luminous efficiency. 
     Although tungsten is used for the mask film  13  of Modification 1, another metal with a high melting point or a metal compound with a high melting point may be used instead. For example, molybdenum (Mo), niobium (Nb), tungsten silicide (Wsi x ), molybdenum silicide (MoSi x ) or niobium silicide (NbSi x ) may be used. Films of these materials can be comparatively easily formed by electron beam deposition or sputtering. 
     Modification 2 of Embodiment 1 
       FIG. 8  shows the sectional structure of a gallium nitride-based semiconductor laser diode according to Modification 2 of Embodiment 1. In  FIG. 8 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     As is shown in  FIG. 8 , in the semiconductor laser diode of Modification 2, the n-type cladding layer  16  of n-type Al 0.07 Ga 0.93 N is directly formed on the seed layer  12  without forming a selectively grown layer and an n-type contact layer therebetween. 
     As described in Embodiment 1, since the grooves  12   b  are formed in the upper portion of the seed layer  12  excluding portions serving as the seed crystal, the gaps  12   c  are formed on the mask film  13 . Therefore, even when polycrystals are deposited on the mask film  13 , the polycrystals are never incorporated into a semiconductor layer selectively grown on the seed layer  12 . As a result, the selectively grown semiconductor layer can attain so good crystallinity that the n-type cladding layer  16  corresponding to a part of the lamination body  30  of the laser structure can be formed directly on the seed layer  12 . In this case, the n-side electrode  24  is provided on an exposed portion of the n-type cladding layer  16 . 
     Embodiment 2 
     Embodiment 2 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 9  shows the sectional structure a gallium nitride-based semiconductor laser diode using the M plane as a cavity facet according to Embodiment 2. In  FIG. 9 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     In the semiconductor laser diode of this embodiment, convexes  11   a  in the shape of stripes for the selective growth are formed in an upper portion of a substrate  11 A of, for example, sapphire along a direction vertical to the M plane of the cavity facet, namely, along the A-axis (=&lt;11-20&gt;) of the substrate  11 A. 
     In this case, an n-type contact layer  15  is characterized by being directly formed by using, as a seed crystal, monocrystal nuclei generated on the C plane of the respective convexes  11   a  of the substrate  11 A. 
     Now, a method of fabricating the semiconductor laser diode having the aforementioned structure will be described with reference to the drawings. 
     FIGS.  10 ( a ),  10 ( b ),  11  and  12  are sectional views for showing procedures in the method of fabricating the semiconductor laser diode of Embodiment 2. 
     First, as is shown in FIG.  10 ( a ), after a resist film is applied on a substrate  11 A having the C plane as the principal plane, the resist film is patterned into stripes by the photolithography, thereby forming a resist pattern  40  in the shape of stripes extending along the A-axis of the substrate  11 A with a cycle of approximately 10 through 30 μm. Subsequently, by using the resist pattern  40  as a mask, grooves  11   b  each with a sectional width of approximately 9 through 27 μm and a depth of approximately 20 through 500 nm are formed in an upper portion of the substrate  11 A by dry etching such as reactive ion etching (RIE). In this embodiment, a convex  11   a  formed between the grooves  11   b  has a sectional width of approximately 1 through 3 μm. 
     Next, as is shown in FIG.  10 ( b ), the resist pattern  40  is removed, so as to obtain the substrate  11 A having, in its upper portion, the convexes  11   a  in the shape of stripes extending along the A-axis. 
     Then, as is shown in  FIG. 11 , after increasing the substrate temperature to approximately 1000° C., trimethyl gallium (TMG), ammonia (NH 3 ) and silane (SiH 4 ) are supplied onto the substrate  11 A in, for example, a mixed atmosphere of hydrogen and nitrogen at a pressure of approximately 100 Torr (1 Torr=133.322 Pa), so as to grow an n-type contact layer  15  of n-type GaN on the substrate  11 A by the MOVPE by using, as the seed crystal, monocrystal nuclei generated on the C plane appearing on the top faces of the convexes  11   a . At this point, the n-type contact layer  15  is grown not only upward from the top faces of the convexes  11   a  but also along a direction parallel to the substrate surface. The crystals grown from the both sides of the groove  11   b  meet each other so as to form a junction portion  15   a  at substantially the center of the groove  11   b . In this manner, the crystals grown from the top faces of the plural convexes  11   a  are integrated, so as to form the n-type contact layer  15  having the C plane as the top face. Also at this point, plural gaps  11   c  are formed so as to be surrounded with the bottoms and the walls of the respective grooves  11   b  and the lower face of the n-type contact layer  15 . 
     Now, growth mechanism in the selective growth by using the substrate  11 A of sapphire will be described. 
     In growing a nitride semiconductor in general on a substrate having a different lattice constant from the nitride semiconductor, if GaN crystal is directly grown on the substrate without forming a low temperature buffer layer of a nitride semiconductor therebetween, merely a three-dimensional film including a combination of monocrystal nuclei of GaN is formed. 
     On the other hand, according to this embodiment, since the dry etching is employed for forming the grooves  11   b  of the substrate  11 A, damage layers derived from the dry etching are formed on the bottoms and the walls of the grooves  11   b . Therefore, generation of the monocrystal nuclei are prevented on the bottoms and the walls of the grooves  11   b . Furthermore, the top face of each convex  11   a  not subjected to the dry etching has a small sectional width of approximately 1 through 3 μm, and hence, monocrystal nuclei with a high density can be easily generated thereon. In this manner, the monocrystal nuclei generated on the top faces of the convexes  11   a  work as the seed crystal for the selective growth, resulting in accelerating the selective growth along the substrate surface direction under the aforementioned conditions. 
     In  FIG. 11 , threading dislocations are observed in a selectively grown region excluding the junction portions  15   a  at a density of approximately 1×10 6  cm −2  while dislocations horizontal to the C plane are observed in the junction portions  15   a  at a density of approximately 4×10 7  cm −2 . The thickness of the n-type contact layer  15  depends upon the width and the like of the groove  11   b  and is herein approximately 2 through 6 μm. Also, a tilt angle between the C-axis in-a portion of the n-type contact layer  15  above the convex  11   a  and the C-axis in a portion thereof above the gap  11   c  is suppressed to 0.01 through 0.03 degree. 
     The tilt angle can be thus very small in the ELOG of this embodiment as compared with that in the conventional ELOG because the n-type contact layer  15  corresponding to the crystal layer formed through the ELOG is not in contact with the substrate  11 A, and hence, stress as in the conventional ELOG is not applied to the interface with the mask film  13 . 
     At this point, a void in the shape of a reverse V having an opening on the gap  11   c  is formed in a lower portion of the junction portion  15   a.    
     Furthermore, in this embodiment, even when polycrystals are deposited on the bottoms of the grooves  11   b  in the selective growth of then-type contact layer  15 , the polycrystals are never in contact with the n-type contact layer  15  owing to a level difference caused between the convex  11   a  and the groove  11   b  formed in the upper portion of the substrate  11 A. Therefore, the crystal quality of the lamination body  30  is never harmfully affected. As a result, variation in the operation characteristic of the laser diode including the lamination body  30  can be reduced, so as to improve the yield. 
     Next, as is shown in  FIG. 12 , the rest of semiconductor layers of the lamination body  30  are formed on the n-type contact layer  15 . 
     Specifically, after setting the substrate temperature to, for example, approximately 970° C., an n-type cladding layer  16 , an n-type light guiding layer  17 , a MQW active layer  18 , a p-type light guiding layer  19 , a p-type cladding layer  20  and a p-type contact layer  21  are successively grown on the n-type contact layer  15  in a mixed atmosphere of hydrogen and nitrogen at a pressure of approximately 300 Torr. In this case, the MQW active layer  18  includes a well layer of Ga 0.92 In 0.08 N with a thickness of approximately 4 nm and a barrier layer of GaN with a thickness of approximately 6 nm. 
     Subsequently, as is shown in  FIG. 9 , an upper portion of the p-type cladding layer  20  and the p-type contact layer  21  are formed into a ridge  31  for selectively injecting a current into the MWQ active layer  18  in a direction along the M-axis (=&lt;1-100&gt;) of the lamination body  30 , namely, in a direction parallel to the grooves  11   b  of the substrate  11 A in a region positioned above the gap  11   c  and not overlapping the junction portion  15   a , namely, in a dislocation low-density region. In this case, the ridge  31  has a width of approximately 2 through 5 μm. 
     Since GaN crystal is transparent against visible light, it is easy to distinguish the convex  11   a  from the gap  11   c  with an optical microscope. Therefore, in determining the position of the ridge  31  in the photolithography, there is no need to use a dedicated alignment pattern. 
     Next, after partly exposing the n-type contact layer  15  by masking the lamination body  30  excluding the ridge  31 , an insulating film  22  is deposited on the exposed faces of the lamination body  30 . Then, a p-side electrode  23  is formed on the insulating film  22  so as to extend over the ridge  31  and cover a portion of the p-type contact layer  21  exposed from the insulating film  22 . Also, an n-side electrode  24  is formed on a portion of the n-type contact layer  15  exposed from the insulating film  22 . 
     Then, the substrate  11 A is cleaved on the M plane of the lamination body  30 , namely, on it&#39;s A plane, thereby forming a cavity facet. Although the A plane of sapphire is a crystal plane difficult to cleave-as described above, even when the sapphire crystal is broken with the cleavage shifted from a predetermined position, the breakage is prevented from being propagated to the lamination body  30  owing to the gaps  11   c  formed in the substrate  11 A. Accordingly, a good cleaved end can be easily obtained in the vicinity of the cavity facet. The yield in the cleavage of the laser diode can be thus improved. 
     Next, the cleaved end of the cavity is coated with a dielectric film or the like so as to attain appropriate reflectance, and thereafter, the substrate is divided along a plane parallel to the ridge  31  into chips so as to obtain semiconductor laser diodes. 
     In the semiconductor laser diode of this embodiment, uniform step flow growth is observed in the ELO grown region as described in Embodiment 1. When the MQW active layer  18  is grown on such a flat surface, local segregation of indium can be avoided. As a result, the MQW active layer  18  is formed as a high quality crystal, so as to reduce the operation current of the laser diode. 
       FIG. 13  shows a far-field pattern, in a direction parallel to the cavity facet, of laser emitted from the semiconductor laser diode of this embodiment, and thus, a unimodal distribution of light intensity can be satisfactorily obtained. On the other hand, the far-field pattern of the semiconductor laser diode of Conventional Example 1 exhibits a multimodal distribution of light intensity as shown in FIG.  42 . 
     The semiconductor laser diode of this embodiment attains the unimodal distribution because the gaps  11   c  provided between the lamination body  30  and the substrate  1 A can optically separate the lamination body  30  and the substrate  11 A from each other. 
     Specifically, as is shown in  FIG. 9 , since the n-type contact layer  15  having a large refractive index than the n-type cladding layer  16  is formed under the n-type cladding layer  16 , light generated in the MQW active layer  18  can easily leak to the substrate  11 A. However, in this embodiment, since the gaps  11   c  with a very small refractive index are formed below the n-type contact layer  15 , a parasitic waveguide is never formed between the n-type cladding layer  16  and the substrate  11 A. As a result, the light confinement coefficient of the MQW active layer  18  is never lowered by the leakage of the generated light. 
     This effect to suppress the formation of a parasitic waveguide depends upon a dimension of the gap  11   c  along a direction vertical to the substrate surface, namely, the depth of the groove  11   b . According to computer simulation, it is confirmed that the leakage of light to the substrate  11 A can be substantially avoided when the depth of the groove  11   b  is at least approximately 50 nm. 
     It is also confirmed that when the n-type contact layer  15  of GaN includes 2% or more of aluminum, the leakage of light to the substrate  11 A can be more effectively avoided. 
     Although gallium nitride is used as the monocrystal nuclei generated on the top faces of the convexes  11   a  of the substrate  11 A in this embodiment, the monocrystal nucleus may be another gallium nitride-based mixed crystal, namely, Al u Ga v In w N, wherein 0≦u, v, w≦1 and u+v+w=1. When the mixed crystal is used, the optimal conditions for the ELOG can be appropriately selected in accordance with the composition of the mixed crystal. 
     Although sapphire is used for the substrate  11 A in this embodiment, for example, silicon carbide, gallium nitride or the like may be used instead of sapphire. However, when the substrate  11 A is made from silicon carbide, tensile strain is applied to the lamination body  30  so as to easily cause cracks. Therefore, it is preferred in this case that the integrated n-type contact layer  15  has a thickness smaller than 2 μm by setting the sectional width of each groove  11   b  as small as possible. Furthermore, when the substrate  11 A is made from silicon carbide or gallium nitride, although it can be easily cleaved on the M plane as well as A plane, the yield can be improved by cleaving the substrate on a plane perpendicular to the direction of the stripes of the grooves  11   b.    
     Although the dry etching by the RIE is employed in forming the grooves  11   b  in the substrate  11 A in this embodiment, any other dry etching method, such as ion milling, may be employed as far as a damage layer can be formed on the bottoms and the walls of the grooves  11   b  so as to selectively grow a gallium nitride-based semiconductor. 
     The damage layer formed in the grooves  11   b  is used as a mask layer for the ELOG in this embodiment. In the case where the deposited polycrystals are adhered onto the damage layer, in particular, in the case where the substrate  1 A is made from gallium nitride, a mask film of silicon nitride or the like is preferably formed at least on the bottoms of the grooves  11   b  so as to further improve the selectivity. 
     The material for the mask film  13  is not limited to silicon nitride but may be a dielectric or amorphous insulator as described in Embodiment 1, and is preferably a metal with a high melting point or a metal compound with a high melting point as described in Modification 1 of Embodiment 1. 
     The invention is applied to a laser diode in this embodiment as described so far, but the invention can be applied to a method of growing a semiconductor for obtaining a gallium nitride-based crystal with a low dislocation density. Furthermore, since the seed layer  12  formed on the substrate  11  in Embodiment 1 is not used in this embodiment, the fabrication process can be simplified. 
     Moreover, not only a light emitting device but also another semiconductor device such as an electronic device can be fabricated by using the nitride semiconductor layer including a dislocation low-density region of this embodiment. In this manner, the reliability and the yield of the semiconductor device can be improved. 
     Embodiment 3 
     Embodiment 3 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 14  shows the sectional structure of a gallium nitride-based semiconductor laser diode according to Embodiment 3. In  FIG. 14 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     Herein, structural differences from the structure of Embodiment 1 alone will be described. 
     Aluminum gallium nitride (AlGaN) is used for a selectively grown layer  14 A grown from the top faces of the respective convexes  12   a  of the seed layer  12  to be integrated, and an n-type superlattice cladding layer  16 A having a superlattice structure including n-type AlGaN and n-type GaN also serves as the n-type contact layer  15 . Thus, the light confinement coefficient of the MQW active layer  18  can be increased. 
       FIG. 15  shows the relationship between the distribution of a refractive index on the ridge along a direction vertical to the substrate surface and the distribution of light intensity on a cavity facet in the semiconductor laser diode of this embodiment. Also,  FIG. 16  shows a far-field pattern, along a direction parallel to the cavity facet, of laser emitted from the semiconductor laser diode of this embodiment. 
     In Embodiment 3, each groove  12   b  of the seed layer  12  has a depth of approximately 50 nm, and then-type superlattice cladding layer  16 A has an average composition of Al 0.07 Ga 0.93 N. Furthermore, the structure of the lamination body above the n-type light guiding layer  17  is the same as that of the conventional semiconductor laser diode shown in FIG.  37 . 
     As is understood from  FIG. 15 , no leakage of generated light to the substrate  11  is observed in the semiconductor laser diode of this embodiment. Also, the light confinement coefficient of the MQW active layer  18  is confirmed to be approximately 1.54 times as large as that shown in FIG.  41 . 
     This is because the MQW active layer  18  is separated from the substrate  11  by the gaps  12   c  of the seed layer  12  and the selectively grown layer  14 A of n-type AlGaN having a refractive index smaller than or equal to the n-type superlattice cladding layer  16 A is provided between the n-type superlattice cladding layer  16 A and the seed layer  12 . Accordingly, no parasitic waveguide is formed between the n-type superlattice cladding layer  16 A and the substrate  11 , and the light confinement coefficient of the MQW active layer  18  can be suppressed from being lowered due to the leakage of the generated light. 
     This effect to suppress the formation of a parasitic waveguide depends upon a dimension of the gap  11   c  along a direction vertical to the substrate surface, namely, the depth of the groove  11   b . As described above, it is confirmed that the leakage of light to the substrate  11  can be substantially avoided when the depth of the groove  11   b  is at least approximately 50 nm. 
     Furthermore, when the selectively grown layer  14 A includes 2% or more and preferably 4% or more aluminum, the leakage of light to the substrate  11  can be suppressed. 
     Also in this embodiment, even when the ELOG of the selectively grown layer  14 A is continued with polycrystals of AlGaN deposited on the mask film  13 , the crystallinity of the selectively grown layer  14 A is never degraded by the polycrystals because there is a level difference between the top face of the convex  12   a  serving as the seed crystal and the bottom of the groove  12   b  where the polycrystals are deposited. As a result, the variation in the crystallinity of the lamination body  30  can be largely reduced, so as to improve the yield in the fabrication of semiconductor laser diodes. 
     Now, a method of aligning the ridge  31  on the lamination body  30  will be described. 
     In order to form the ridge  31  in a dislocation low-density region of the lamination body  30  above the gap  12   c , it is necessary to accurately align the ridge  31  in the photolithography. 
       FIG. 17  shows a plane photograph of the selectively grown layer  14 A prior to the formation of the lamination body  30  obtained with an optical microscope and the corresponding sectional structure of the selectively grown layer  14 A. As is shown in  FIG. 17 , a dislocation low-density region  14   c  can be easily distinguished from a dislocation high-density region  14   b  and a junction portion  14   a  with the optical microscope. Accordingly, in a procedure for aligning the ridge  31  in the photolithography, there is no need to use a dedicated alignment pattern (alignment mark). 
     Furthermore, it is necessary to cleave the substrate  11  and the lamination body  30  for forming a cavity facet. Also in this embodiment, claws caused in the substrate  11  can be stopped by the gaps  12   c  provided in the seed layer  12 , and hence, the harmful effect on the lamination body  30  can be definitely reduced. 
     In this embodiment, the n-side electrode  24  is in contact with the n-type superlattice cladding layer  16 A and the n-type superlattice cladding layer  16 A also serves as the n-type contact layer. 
     As described above, in order to suppress the leakage of generated light from the MQW active layer  18  to the substrate  11 , it is necessary to form a semiconductor layer including aluminum between the n-type light guiding layer  17  and the gaps  12   c . However, when the n-type contact layer on which the n-side electrode  24  is formed is made from a bulk layer (single layer) including aluminum in a large composition ratio, for example, a single layer of n-type Al 0.07 Ga 0.93 N, the driving voltage of the laser diode is increased because the resistivity of the single layer is increased to approximately twice of that of gallium nitride or the contact resistance is increased. 
     As a result of a variety of examinations, the present inventors have found that the specific resistance of the n-type superlattice cladding layer  16 A including, for example, n-type Al 0.14 Ga 0.86 N and n-type GaN is substantially equal to that of a single layer of n-type GaN. This is because of large mobility of two-dimensional electron gas generated in the superlattice semiconductor layer. Furthermore, the present inventors have found that the contact resistance of the superlattice semiconductor layer can be substantially equal to that of an n-type GaN layer when the thickness of a unit layer included in the superlattice structure is sufficiently small, for example, is approximately 2 nm. At this point, the doping concentration of the n-type impurity is approximately 1×10 18  cm −3 . 
     Accordingly, by forming the superlattice structure from AlGaN and GaN, while making the best use of the small refractive index of AlGaN, low resistance can be simultaneously attained, resulting in definitely attaining a low driving voltage. 
     The superlattice layer preferably includes aluminum in an average ratio of 2% and has a thickness of λ/(4n) or less, wherein λ indicates the wavelength of light and n indicates the refractive index of the unit layer. 
     Moreover, according to this embodiment, uniform step flow growth is observed and satisfactory surface flatness is confirmed in the dislocation low-density region  14   c  of the selectively grown layer  14 A shown in FIG.  17  through the measurement with an atomic-force-microscopy (AFM). As a result, no local segregation of indium is caused in growing the MQW active layer  18  including indium, which reduces the threshold current. 
     Although the substrate  11  is made from sapphire, for example, silicon carbide, neodymium gallate (NGO), gallium nitride or the like may be used instead of sapphire. 
     Although the convexes  12   a  in the seed layer  12  are formed by the lift-off method, any other method may be employed as far as the convexes  12   a  and the grooves  12   b  can be formed with the mask film  13  remaining on at least the bottoms of the grooves  12   b.    
     The mask film  13  may be formed on the bottoms of the grooves  12   b  alone as far as the gaps  12   c  can be formed. 
     Furthermore, the mask film  13  may be formed from a dielectric such as silicon nitride and silicon oxide by the ECR sputtering, and preferably, is formed from a metal with a high melting point such as tungsten or its silicide. 
     Embodiment 4 
     Embodiment 4 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 18  shows the sectional structure of a gallium nitride-based semiconductor laser diode of Embodiment 4. In  FIG. 18 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     Herein, structural differences from the structure of Embodiment 3 alone will be described. 
     In this embodiment, the selectively grown layer  14 A of AlGaN of Embodiment 3 is formed to have a two-layer structure including a first selectively grown layer  14 B of GaN formed in the vicinity of the top faces of the convexes  12   a  of the seed layer  12  and a second selectively grown layer  14 C of AlGaN for covering the top and side faces of the first selectively grown layer  14 B as is shown in FIG.  18 . 
     Furthermore, the n-type superlattice cladding layer  16 A also serving as the n-type contact layer is formed to have a two-layer structure including an n-type superlattice contact layer  15 A and an n-type cladding layer  16  of a single Al 0.07 Ga 0.93 N layer. In this case, the n-type superlattice contact layer  15 A has a superlattice structure including n-type Al 0.01 Ga 0.09 N and n-type GaN. 
     Moreover, the p-side electrode  23  is formed merely on the top face of the ridge  31  formed in the upper portion of the lamination body  30 , and a p-side line electrode  25  is formed so as to cover the p-side electrode  23  and the ridge  31 . Similarly, the n-side electrode  24  is covered with an n-side line electrode  26 . 
     Now, the characteristics of a method of fabricating the semiconductor laser diode of this embodiment will be described. 
     First, plural first selectively grown layers  14 B are grown by using, as the seed crystal, the top faces of the convexes  12   a  of the seed layer  12 . The growth pressure for the first and second selectively grown layers  14 B and  14 C is set to a comparatively low pressure of approximately 200 Torr until the second selectively grown layers  14 C grown by using, as the seed crystal, the first selectively grown layers  14 B are integrated. 
     This is because as the pressure is reduced, the growth rate of the first and second selectively grown layers  14 B and  14 C is larger in the A-axis direction of the seed layer  12 , namely, in a direction crossing the grooves  12   b , than in the C-axis direction vertical to the substrate surface. 
     In contrast, the MQW active layer  18  is grown at a high pressure of approximately 300 Torr. This is because as the growth pressure is higher, indium with a high vapor pressure can be suppressed to evaporate, so that the MQW active layer  18  can attain higher crystal quality. Accordingly, in forming the lamination body  30 , the growth pressure is changed from that for growing the first and second selectively grown layers  14 B and  14 C. 
     In order to change the growth pressure in continuous growth of nitride semiconductors, one crystal growth furnace capable of changing the growth pressure during its operation may be used, or plural crystal growth furnaces respectively set to different growth pressures may be used. 
     The semiconductor laser diode of Embodiment 4 exhibits, similarly to that of Embodiment 3, the refractive index distribution and the light intensity distribution as shown in FIG.  15  and attains the far-field pattern of emitted light as shown in FIG.  16 . 
     This is because the MQW active layer  18  is separated from the substrate  11  by the gaps  12   c  of the seed layer  12 , and the n-type superlattice contact layer  15 A and the second selectively grown layer  14 C having a refractive index smaller than or equivalent to the n-type cladding layer  16 A is formed between the n-type cladding layer  16  and the seed layer  12 . Accordingly, no parasitic waveguide is formed between the n-type cladding layer  16  and the substrate  11 , and the light confinement coefficient of the MQW active layer  18  can be suppressed from being reduced due to the leakage of the generated light. 
     In this embodiment, it is confirmed through computer simulation that the light leakage to the substrate  11  can be substantially avoided when the depth of the groove  12   b  is at least approximately 20 nm. 
     Furthermore, when the second selectively grown layer  14 C includes 2% or more and preferably 4% or more of aluminum, the leakage of the generated light to the substrate  11  can be suppressed. 
     Owing to the aforementioned structure, the light confinement coefficient of the MQW active layer  18  is approximately 1.5 times as large as that shown in  FIG. 41 , resulting in reducing the threshold current of the laser diode. 
     Now, a difference in the growth mechanism between the selective growth of this invention by using the top faces of the convexes  12   a  as the seed crystal and the selective growth of Conventional Example 2 by masking a flat seed layer in the shape of stripes shown in  FIG. 38  will be described. 
     FIG.  19 ( a ) schematically shows the selective growth mechanism of Embodiment 4 and FIG.  19 ( b ) schematically shows the selective growth mechanism of Conventional Example 2. 
     As is well known, during growth of a reaction seed of molecules or the like into a desired crystal, processes of adsorption, diffusion, evaporation and the like of the reaction seed are repeated on the surfaces of the crystal and a mask film. For example, atoms adsorbed onto the surface of a crystal of GaN are diffused over a terrace, that is, the top face of the crystal. Also, atoms adsorbed onto the surface are crystallized on a level difference portion on the terrace designated as a step. 
     As is shown in FIG.  19 ( b ), the similar processes are repeated on the mask film  403  in the conventional ELOG. Specifically, atoms diffused over the mask film  403  are adsorbed on the edge of the semiconductor layer  404  of GaN. At this point, silicon or oxygen included in the mask film  403  is decomposed through a reducing function of hydrogen or ammonia so as to be incorporated into the semiconductor layer  404  as an impurity. This degrades the crystallinity of the semiconductor layer  404 . 
     In contrast in this embodiment, as is shown in FIG.  19 ( a ), no atoms are diffused over the mask film  13  so as to be incorporated into the first selectively grown layer  14 B of GaN. This is because no crystal grows on the lower face of the first selectively grown layer  14 B. Thus, the reaction seed on the mask film  13  makes a different contribution to the crystal growth from that in the conventional ELOG, which differs the growth mechanism of this invention from that of the conventional ELOG. 
     Although the first selectively grown layer  14 B is formed from GaN and the second selectively grown layer  14 C is formed from Al 0.05 Ga 0.95 N in this embodiment, the first selectively grown layer  14 B may be formed from any nitride semiconductor including 4% or less of aluminum and represented by Al x Ga y In z N, wherein x+y+z=1. 
     Now, the purpose of forming the first selectively grown layer  14 B by using the seed layer  12  as the seed crystal before growing the second selectively grown layer  14 C with a small refractive index will be described with reference to the drawings. 
     As described in Embodiment 3, there is no need to form the selectively grown layer in a two-layer structure merely for controlling the lateral mode in a direction vertical to the substrate surface and increasing the light confinement coefficient of the MQW active layer  18 . 
     However, in the case where the selectively grown layer  14 A of AlGaN includes 4% or more of aluminum, roughness  14   d  may be caused at the end in the growing direction of the selectively grown layer  14 A as is shown in FIG.  20 ( b ). Such roughness maybe rather suppressed by appropriately setting the growth conditions for the selectively grown layer  14 A, such as a growth pressure, a growth temperature and a V/III ratio, that is, a molar ratio between a group III element source and a group V element source. However, in consideration of mass production, the roughness  14   d  at the growth end is preferably minimized as far as possible. 
     The present inventors have found that a nitride semiconductor layer including aluminum in a small composition ratio is preferably used for the selectively grown layer formed by using the seed layer  12  as the seed crystal. 
     Specifically, as is shown in FIG.  20 ( a ), the first selectively grown layer  14 B of a gallium nitride-based semiconductor including 4% or less of aluminum is first grown in the vicinity of the convexes  12   a  of the seed layer  12 , and then, the second selectively grown layer  14 C of a gallium nitride-based semiconductor including more than 4% of aluminum and having a small refractive index is grown by using the first selectively grown layer  14 B as the seed crystal. In this manner, the second selectively grown layer  14 C can be satisfactorily laterally grown without causing the roughness  14   d  at the growth end. 
     Furthermore, as the composition ratio of aluminum is larger in the second selectively grown layer  14 C and as the growth time is longer, more polycrystals  41  are deposited on the mask film  13 . This is because the evaporation rate of the AlGaN crystal or the AlN crystal is smaller than that of the GaN crystal. 
     As is shown in FIGS.  21 ( a ) through  21 ( d ), since the first selectively grown layer  14 B of GaN causing less deposition of the polycrystals  41  is first grown, the growth time required for integrating the growth ends of the second selectively grown layers  14 C can be shortened. 
     Moreover, since the first selectively grown layer  14 B is grown in the shape of an umbrella as shown in FIG.  21 ( c ), the quantity of the reaction seed supplied onto the mask film  13  can be reduced. Accordingly, the quantity of the polycrystals  41  deposited on the mask film  13  can be largely reduced, so as to minimize the harmful effect on the lamination body  30  grown above the gaps  12   c . As a result, the light confinement coefficient can be definitely increased, and the production yield can be definitely improved because the crystallinity of the lamination body  30  is so improved that the variation in the operation characteristic of the laser diode is largely reduced. 
     Although the substrate  11  is made from sapphire in this embodiment, for example, silicon carbide, neodymium gallate, gallium nitride or the like may be used instead of sapphire. 
     Also, the mask film  13  can be formed merely on the bottoms of the grooves  12   b  as far as the gaps  12   c  can be formed. 
     Furthermore, the mask film  13  may be formed from a dielectric such as silicon nitride and silicon oxide by the ECR sputtering, and more preferably, is formed from a metal with a high melting point such as tungsten or its silicide. 
     Embodiment 5 
     Embodiment 5 of this invention will now be described with reference to the accompanying drawings. 
       FIGS. 22 and 23  show a gallium nitride-based semiconductor laser diode according to Embodiment 5, wherein  FIG. 22  shows the sectional structure taken on the M plane of a lamination body, namely, the A plane of a substrate, and  FIG. 23  shows the sectional structure taken on line XXIII—XXIII of  FIG. 22  corresponding to the A plane of the lamination body, namely, the M plane of the substrate. In  FIGS. 22 and 23 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     Embodiment 5 is characterized by definitely fabricating a semiconductor laser diode with a flat cavity facet  32  by using the lamination body  30  including the MQW active layer  18 . 
     As is shown in  FIG. 22 , in an upper portion of the seed layer  12 , a cyclic structure including, as one cycle, the convex  12   a  with a sectional width of approximately 3 μm and the groove  12   b  with a sectional width of approximately 12 μm is formed, and every 34 cycles (corresponding to a length of 510 μm) of the cyclic structure, an enlarged groove  12   d  with an enlarged sectional width of approximately 20 μm is formed. 
     When the lamination body  30  is formed in the same manner as in Embodiment 1, the lamination bodies  30  laterally grown by using the top faces of the respective convexes  12   a  of the seed layer  12  as the seed crystal are not integrated above the enlarged groove  12   d . Therefore, the A planes of the adjacent lamination bodies  30  appear above the enlarged groove  12   d  without being in contact with each other. These growth ends are naturally formed crystal planes, and includes no other surface orientations such as the M plane. Accordingly, when such a growth end is used as the cavity facet  32 , the mirror loss on the cavity facet derived from mixture of the A plane and the M plane as in the conventional semiconductor laser diode of  FIG. 43  can be avoided. 
     When the growth end with the naturally formed A plane is observed with an atomic-force-microscopy (AFM), it is confirmed that the end has a very flat surface with an average of a square of the roughness smaller than 1 nm. 
     Furthermore, when the growth end is used as the cavity facet  32 , the P-type light guiding layer  19  and the p-type cladding layer  20  with larger energy gap than the MQW active layer  18  can be formed on the cavity facet  32 . Therefore, emitted light is never absorbed at the ends of the p-type light guiding layer  19  and the p-type cladding layer  20 . As a result, the temperature increase in the lamination body  30  in the vicinity of the cavity facet  32  can be suppressed, and hence, the reliability can be prevented from degrading due to degradation of the facet. 
     In the semiconductor laser diode of Embodiment 5, the ELOG using the top faces of the convexes  12   a  in the shape of stripes as the seed crystal is employed, and the enlarged grooves  12   d  are formed in a cycle larger than that of the grooves  12   b  formed by the side faces of the convexes  12   a . Therefore, the growth end of the lamination body  30  is directly exposed above the enlarged groove  12   d , and hence, the naturally formed exposed end can be formed into the cavity facet  32 . When the semiconductor laser diode having such a cavity facet is compared with the semiconductor laser diode of Conventional Example 2 of  FIG. 39  in the threshold value for laser action, the threshold value of the laser diode of this embodiment is lower by approximately 30% than that of the conventional laser diode. 
     Although the substrate  11  is formed from sapphire in this embodiment, for example, silicon carbide, neodymium gallate (NGO), gallium nitride or the like may be used instead of sapphire. 
     Also, the mask film  13  may be formed merely on the bottoms of the grooves  12   b  as far as the gaps  12   c  can be formed. 
     Furthermore, the mask film  13  may be formed from a dielectric such as silicon nitride and silicon oxide by the ECR sputtering, and more preferably, is formed from a metal with a high melting point such as tungsten or its silicide. 
     Moreover, the widths of the convex  12   a  and the groove  12   b  formed in the upper portion of the seed layer  12  are not limited to 3 μm and 12 μm, respectively but the convex  12   a  preferably has a smaller width than the groove  12   b . In this manner, the influence of dislocations propagated from the seed crystal on the top faces of the convexes  12   a  to the lamination body  30  can be reduced, and the degradation of the laser operation characteristics due to the dislocations can be prevented, resulting in improving the reliability of the laser diode. 
     Also, the cycle of forming the enlarged grooves  12   d  in the upper portion of the seed layer  12  may be set to an appropriate value in accordance with the length of the cavity. 
     In Embodiment 5, the stripe direction of the convexes  12   a  is set to the M-axis direction of the lamination body  30  so as to use the naturally formed A plane as the cavity facet  32 . Instead, when the stripe direction of the convexes  12   a  is set to the A-axis direction perpendicular to the M-axis of the lamination body  30 , the M plane can be naturally formed. Accordingly, when the convexes  12   a  are formed in the shape of stripes extending along the A-axis direction, a highly reliable semiconductor laser diode including the naturally formed M plane as the cavity facet  32  and having a largely reduced threshold current can be obtained. 
     Modification 1 of Embodiment 5 
     Modification 1 of Embodiment 5 will now be described with reference to the accompanying drawing. 
       FIG. 24  shows the sectional structure of a gallium nitride-based semiconductor laser diode of Modification 1 of Embodiment 5 taken on the M plane of a lamination body, namely, the A plane of a substrate. In  FIG. 24 , like reference numerals are used to refer to like elements shown in FIG.  22 . 
     As is shown in  FIG. 24 , in the semiconductor laser diode of Modification 1, an enlarged groove  12   d  with an enlarged sectional width of approximately 20 μm is formed on the inside of and adjacent to the enlarged groove  12   d  for naturally forming the cavity facet  32  of the lamination body  30 . Accordingly, side gaps  30   a  having the A plane as the opposing faces are formed on both sides of the lamination body  30  close to the cavity facets. 
     Since the side gap  30   a  having a refractive index of 1 and the lamination body  30  of a gallium nitride-based semiconductor having a refractive index of approximately 2.6 are combined to form the cavity facet  32 , a large difference in the refractive index can be obtained. Accordingly, the reflectance of a laser beam on the cavity facet  32  can be increased as compared with the case where the cavity facet is coated with a dielectric film or the like. 
     For the purpose of increasing the reflectance of a laser beam on the cavity facet  32 , an isolation body isolated from the lamination body  30  by the side gap  30   a  preferably has a lateral dimension, along the light emitting direction, of an integral multiple of λ/(4n), wherein λ indicates the wavelength of light and n indicates the refractive index of the isolation body. 
     Although the side gaps  30   a  are formed on both sides of the lamination body  30  in this modification, the side gap  30   a  may be formed on either side of the lamination body  30  for increasing the reflectance so as to increase the output power of emitted light. 
     According to this modification, the threshold current for laser action is reduced by approximately 20% as compared with the case where the side gaps  30   a  are not formed, and thus, the effect attained by the side gaps  30   a  is remarkable. It is noted that the lamination body  30  may include three or more side gaps  30   a.    
     Modification 2 of Embodiment 5 
       FIG. 25  shows Modification 2 of Embodiment 5, wherein all the grooves in the shape of stripes formed in the upper portion of the seed layer  12  are formed as enlarged grooves  12   d.    
     In this manner, plural lamination bodies  30  are all isolated from one another on the substrate  11 . Accordingly, when a cavity is formed from plural isolation bodies so as to obtain a desired cavity length and the substrate  11  is divided in a side gap  30   a  in a position corresponding to the facet of the thus formed cavity, one semiconductor laser diode including plural isolation bodies can be obtained. 
     Accordingly, the semiconductor laser diode of Modification 2 has a very flat A plane free from irregularities causing mirror loss of a laser beam, and when the number of isolation bodies included in the laser diode is changed, the cavity length can be easily changed. 
     Furthermore, when the substrate  11  is divided in every enlarged groove  12   d , a laser diode including one convex  12   a  and having a cavity length of approximately 15 μm can be obtained. In a conventional technique to simultaneously cleave a substrate and a lamination body, it is very difficult to fabricate such a small cavity with keeping the flatness of the cavity facet. 
     Modification 3 of Embodiment 5 
     In Modification 3 of Embodiment 5, convexes in the shape of stripes are further formed in an upper portion of a selectively grown layer so as to completely eliminate crystal dislocations from the lamination body  30 . Thus, the reliability of the semiconductor laser diode can be further improved. 
     As is shown in  FIG. 26 , on a seed layer  12  having convexes  12   a  and grooves  12   b  in the upper portion with a first mask film  13 A formed on the bottoms and the walls of the grooves  12   b , a selectively grown seed layer  34  is integrally formed through the ELOG. 
     In an upper portion of the selectively grown seed layer  34 , convexes  34   a  and grooves  34   b  are formed in an equivalent cycle of the convexes  12   a  and the grooves  12   b  of the seed layer  12 , and a second mask film  13 B is formed on the bottoms and the walls of the grooves  34   b.    
     In this case, the convexes  34   a  are formed above the grooves  12   b  so as to be formed neither in a dislocation low-density region nor in a junction portion of the selectively grown seed layer  34 . 
     In this manner, according to Modification 3, the selectively grown layer  14  is grown by using, as the seed crystal, the C plane on the top faces of the convexes  34   a  formed in the upper portion of the selectively grown seed layer  34 . On the top face of the convex  34   a  appears a high quality crystal face free from not only dislocations derived from the seed crystal on the top face of the convex  12   a  of the seed layer  12  but also a defect derived from the junction portion of the selectively grown seed layer  34 . As a result, the lamination body  30  formed on the high quality selectively grown layer  14  is free from defectives. Accordingly, it is possible to avoid loss resulting from scatter of a laser beam due to a crystal defective and degradation of the reliability through a non-luminescent process of carriers. Thus, this modification realizes a very high quality gallium nitride-based semiconductor laser diode. 
     Embodiment 6 
     Embodiment 6 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 27  shows the sectional structure of a gallium nitride-based semiconductor laser diode of Embodiment 6 taken on the A plane of a lamination body, namely, the M plane of a substrate. In  FIG. 27 , like reference numerals are used to refer to like elements used in Embodiment 3 shown in  FIG. 14  so as to omit the description. 
     Herein, structural differences from the structure of Embodiment 3 alone will be described. 
     As is shown in  FIG. 27 , a first seed layer  12 A and a second seed layer  12 B are formed on the substrate  11  of sapphire. 
     In an upper portion of the first seed layer  12 A, convexes  12   a  and grooves  12   b  in the shape of stripes are formed in parallel to the M plane of the substrate  11 , namely, the A plane of the lamination body  30 . Similarly, in an upper portion of the second seed layer  12 B, the convexes  12   a  and the grooves  12   b  in the shape of stripes are formed in parallel to the convexes  12   a  and the grooves  12   b  of the first seed layer  12 A so as not to overlap them in a direction vertical to the substrate surface. 
     Now, a method of fabricating the semiconductor laser diode having the aforementioned structure will be described with reference to the drawings. 
     FIGS.  28 ( a ),  28 ( b ),  29 ( a ),  29 ( b ),  30 ( a ),  30 ( b ) and  31  are sectional views taken on the A plane of the substrate for showing procedures in the method of fabricating the semiconductor laser diode of this embodiment. 
     First, as is shown in FIG.  28 ( a ), a low temperature buffer layer (not shown) of GaN is deposited on a substrate  11  having the C plane as the principal plane by the MOVPE by supplying TMG as a group III element source and NH 3  as a nitrogen source with the substrate temperature set to approximately 530° C. in a mixed atmosphere of hydrogen and nitrogen, for example, at a pressure of approximately 300 Torr. Subsequently, after the substrate temperature is increased to approximately 970° C., TMG, NH 3  and SiH 4  are supplied onto the substrate  11 , thereby growing a first seed layer  12 A of n-type GaN with a thickness of approximately 0.5 through 1 μm. At this point, the principal plane of the first seed layer accords with the C plane, and the order of a dislocation density is 10 9  cm −2 . 
     Next, as is shown in FIG.  28 ( b ), after applying a resist film on the first seed layer  12 A, the resist film is patterned by the photolithography into stripes extending along the M-axis direction of the first seed layer  12 A, thereby forming a resist pattern  40 . Subsequently, by using the resist pattern  40  as a mask, the first seed layer  12 A is dry etched, thereby forming, in an upper portion of the first seed layer  12 A, a cyclic structure including, as one cycle, a convex  12   a  with a sectional width of approximately 3 through 6 μm and a groove  12   b  with a sectional width of approximately 12 through 24 μm. At this point, the groove  12   b  has a depth of approximately 50 nm through 1 μm. 
     Then, as is shown in FIG.  29 ( a ), a mask film  13  of silicon nitride is deposited on the bottoms and the walls of the grooves  12   b  of the first seed layer  12 A and the resist pattern  40  by the ECR sputtering. Also in this case, solid silicon is used as the raw material for silicon, nitrogen is used as a reaction gas, and argon is used as plasma gas. 
     Next, as is shown in FIG.  29 ( b ), the resist pattern  40  is lifted off, thereby removing the resist pattern  40  and a portion of the mask film  13  deposited on the resist pattern  40 . The mask film  13  may cover whole or a part of the wall of the groove  12   b.    
     Then, as is shown in FIG.  30 ( a ), after increasing the substrate temperature to approximately 1000° C., TMG, NH 3  and SiH 4  are supplied onto the first seed layer  12 A by the MOVPE again in a mixed atmosphere of hydrogen and nitrogen, for example, at a pressure of approximately 100 Torr, so as to grow a second seed layer  12 B of n-type GaN by using, as the seed crystal, portions of the first seed layer  12 A exposed from the mask film  13 . At this point, the second seed layer  12 B grows upward from the top faces of the convexes  12   a  as well as laterally grows in a direction parallel to the substrate surface. The crystals grown from the both sides of the groove  12   b  meet at substantially the center of the groove  12   b  so as to form a junction portion  12   e . In this manner, the respective crystals grown from the top faces of the plural convexes  12   a  are integrated one another, so as to form the second seed layer  12 B having the C plane as the top face. Also, at this point, plural gaps  12   c  are formed to be surrounded with the bottoms and the walls of the grooves  12   b  of the first seed layer  12 A and the lower face of the second seed layer  12 B. The thickness of the second seed layer  12 B depends upon the width and the like of the groove  12   b  and is approximately 2 through 6 μm. 
     In a selectively grown region of the second seed layer  12 B excluding the junction portions  12   e , threading dislocations are observed at a dislocation density of approximately 1×10 6  cm −2 , while crystal dislocations are observed in the junction portion  12   e  in a dislocation density, in a direction parallel to the C plane, of approximately 4×10 7  cm −2 . 
     Furthermore, a tilt angle between the C-axis in a portion of the second seed layer  12 B above the convex  12   a  and the C-axis in a portion thereof above the gap  12   c  is 0.01 through 0.03 degree. 
     The tilt angle is thus very small in the ELOG of this embodiment as compared with that in the conventional ELOG because the second seed layer  12 B corresponding to a crystal layer formed through the ELOG is not in contact with the first seed layer  12 A and hence no stress is applied to the interface with the mask film  13  differently from the conventional ELOG. 
     It is noted that a void in the shape of a reverse V having an opening on the gap  12   c  is formed in a lower portion of the junction portion  12   e.    
     Furthermore, according to this embodiment, even when polycrystals are deposited on the bottoms of the grooves  12   b  in the selective growth of the second seed layer  12 B, the polycrystals are not in contact with the second seed layer  12 B owing to a level difference caused by the convexes  12   a  and the grooves  12   b  formed in the upper portion of the first seed layer  12 A, and hence do not harmfully affect the crystallinity of a lamination body  30  including the laser structure. As a result, the variation in the operation characteristics of the laser diode including the lamination body  30  can be reduced, so as to improve the yield. 
     Next, as is shown in FIG.  30 ( b ), a cyclic structure including, as one cycle, the convex  12   a  and the groove  12   b  is formed in the upper portion of the second seed layer  12 B in the same manner as in the first seed layer  12 A. At this point, it is preferred that the convexes  12   a  of the second seed layer  12 B are formed so as to have their top faces positioned above the dislocation low-density regions of the second seed layer  12 B. Specifically, the top faces of the convexes  12   a  of the second seed layer  12 B are formed in positions different from the top faces of the convexes  12   a  of the first seed layer  12 A in a direction along the substrate surface and on sides of the junction portions  12   e.    
     In this manner, the second ELOG can be conducted by using, as the seed crystal, the dislocation low-density regions of the second seed layer  12 B positioned above the gaps  12   c  of the first seed layer  12 A. Since a gallium nitride-based crystal is transparent against visible light, the convex  12   a  and the groove  12   b  can be easily identified from each other with an optical microscope. Therefore, there is no need to use a dedicated alignment pattern in determining the positions of the convexes  12   a  in the stripe pattern in the photolithography. 
     Then, as is shown in  FIG. 31 , selectively grown layers  14 A of n-type AlGaN having the C plane as the principal plane are grown to be integrated on the second seed layer  12 B by the MOVPE in, for example, a mixed atmosphere of hydrogen and nitrogen at a pressure of approximately 100 Torr at a substrate temperature of approximately 1000° C. by using, as the seed crystal, the C plane appearing on the top faces of the convexes  12   a  exposed from the mask film  13 . In this manner, in all the regions of the selectively grown layers  14 A excluding junction portions  14   a  cyclically formed, the dislocation density is as small as approximately 1×10 6  cm −2 . 
     Subsequently, in a mixed atmosphere of hydrogen and nitrogen at a pressure of approximately 300 Torr and at a substrate temperature of approximately 970° C., an n-type superlattice cladding layer  16 A, an n-type light guiding layer  17 , a MQW active layer  18 , a p-type light guiding layer  19 , a p-type cladding layer  20  and a p-type contact layer  21  are successively grown on the integrated selectively grown layer  14 A, so as to form the lamination body  30 . At this point, the MQW active layer  18  includes, for example, a well layer of Ga 0.92 In 0.08 N with a thickness of approximately 4 nm and a barrier layer of GaN with a thickness of approximately 6 nm, so as to show laser action at a wavelength of 400 nm band. 
     Thereafter, as is shown in  FIG. 27 , a ridge  31  with a width of 2 through 5 μm for selectively injecting a current into the MQW active layer  18  is formed in the A-axis direction of the lamination body  30 , namely, in a direction perpendicular to the direction of the stripes of the convexes  12   a  by the dry etching from an upper portion of the p-type cladding layer  20  and the p-type contact layer  21 . 
     Subsequently, the lamination body  30  excluding the ridge  31  is dry etched, so as to partly expose the n-type superlattice cladding layer  16 A, and an insulating film  22  is deposited on the exposed faces of the lamination body  30 . Then, openings are formed in the insulating film  22  in positions on the ridge  31  and the n-type superlattice cladding layer  16 A. Thereafter, a p-side electrode  23  is formed on a portion on the ridge  31  exposed in the opening of the insulating film  22  and around the ridge  31 , and an n-side electrode  24  is formed on a portion of the n-type superlattice cladding layer  16 A exposed in the opening of the insulating film  22  by the evaporation or the sputtering. 
     Next, a cavity facet is formed through the cleavage on the A plane of the lamination body  30 , namely, on the M plane of the substrate  11  of sapphire. Since the M plane of sapphire can be easily cleaved, the yield in the cleavage of the semiconductor laser diode can be satisfactorily retained. Although the plural gaps  12   c  in two stages extending in parallel to the cleaved end are present between the substrate  11  and the lamination body  30 , these gaps  12   c  never lower the yield in the cleavage. 
     Then, the cleaved end is coated with a dielectric or the like so as to attain appropriate reflectance, and the substrate is divided into chips. Thus, the semiconductor laser diode of  FIG. 27  is fabricated. 
     As a characteristic of the semiconductor laser diode of Embodiment 6, the cavity formed in the A-axis direction of the lamination body  30  including the MQW active layer  18  is provided in a direction perpendicular to the gaps  12   c  formed through the selective growth in the shape of stripes extending in the M-axis direction. 
     In this case, as is understood from  FIG. 31 , the current injecting region for the MQW active layer  18  extending in the lengthwise direction of the ridge  31  crosses the junction portion  14   a  of the semiconductor layers. As a result, dislocations collected in the junction portion  14   a  can affect the operation of the laser diode. It is, however, confirmed through observation of dislocations within the MQW active layer  18  that threading dislocations are present on the plane uniformly at a density of approximately 1×10 6  cm −2  regardless of the junction portion  14   a . Accordingly, the current injecting region crossing the junction portion  14   a  does not harmfully affect the reliability of the semiconductor laser diode. 
     Furthermore, when a tilt is present in the C-axis between the second seed layer  12 B serving as the seed crystal and the selectively grown layer  14 A, a zigzag waveguide waving in the direction vertical to the substrate surface is formed so as to cause guide loss in the cavity formed in the A-axis direction. As a result, the operation current of the laser diode can be increased. Actually, in a laser diode fabricated by the conventional ELOG as shown in  FIG. 38 , a tilt angle is as large as 0.1 degree or more. Therefore, when the width of the gap  12   c  is, for example, 12 μm, a zigzag waveguide with a level difference of 10 nm or more is formed, resulting in increasing the operation current of the laser diode. 
     On the other hand, when the tilt angle is 0.05 degree or less, the level difference in the waveguide can be suppressed to approximately 5 nm, and hence, the influence of the zigzag waveguide can be substantially ignored. According to this embodiment, the tilt angle can be suppressed to 0.03 degree or less owing to the lateral growth where the selectively grown layer is grown with forming the gaps  12   c , and hence, the formation of the zigzag waveguide can be avoided. 
     Moreover, uniform step flow growth is observed in a laterally grown region of the selectively grown layer  14 A. When the MQW active layer  18  is formed on such a flat face, local segregation of indium can be prevented, so as to obtain the MQW active layer  18  with uniform quality. Accordingly, the operation current can be reduced. 
     The far-field pattern, in the direction vertical to the substrate surface, of the semiconductor laser diode of this embodiment is equivalent to that shown in  FIG. 16 , and thus, a unimodal and satisfactory light intensity distribution can be obtained. 
     This is because, similarly to Embodiment 3, the selectively grown layers  14 A grown from the top faces of the convexes  12   a  of the second seed layer  12 B to be integrated are formed from n-type AlGaN, and the n-type superlattice cladding layer  16 A having the superlattice structure including n-type AlGaN and n-type GaN also works as the n-type contact layer. Thus, the light confinement coefficient of the MQW active layer  18  can be largely increased. 
     As described above, when the selectively grown layer  14 A includes 2% or more and preferably 4% or more of aluminum, the leakage of light to the substrate  11  can be definitely prevented. 
     Although the first and second seed layers  12 A and  12 B are formed from GaN in this embodiment, these seed layers may be made from a gallium nitride-based mixed crystal represented by a general formula, Al u Ga v In w N (wherein 0≦u, v, w≦1 and u+v+w=1), and in particular, AlGaN or GaInN. The optimal growth conditions for the lateral growth are selected in accordance with the composition of the mixed crystal to be used. 
     Furthermore, although the low temperature buffer layer is formed below the first seed layer  12 A, the low temperature buffer layer is not always necessary as far as the first seed layer can be formed in a monocrystal. 
     Although the substrate  11  is made from sapphire, for example, silicon carbide, neodymium gallate (NGO), gallium nitride or the like may be used instead of sapphire. However, when the substrate  11  is made from silicon carbide, tensile strain is applied to the lamination body  30  and hence cracks can be easily caused. Therefore, it is preferred in this case that the integrated second seed layer  12 B has a thickness smaller than 2 μm by reducing the sectional width of the groove  12   b  as far as possible. In this manner, the lamination body  30  can be free from cracks even after the two selective growths and the growth of the lamination body  30 . 
     Accordingly, regardless of the material for the substrate  11 , three or more selective growths are not only meaningless but also unpreferable because new problems derived from strain can be caused. 
     Although the lift-off method is employed in forming the convexes  12   a  in the upper portions of the first and second seed layers  12 A and  12 B, any other method can be employed instead as far as the convexes  12   a  and the grooves  12   b  can be formed with the mask film  13  remaining at least on the bottoms of the grooves  12   b . Specifically, any other method can be employed as far as the C plane on the portions of the convexes  12   a  not covered with the mask film  13  can be used as the seed crystal and the gaps  12   c  can be formed. 
     The material for the mask film  13  is not limited to silicon nitride but can be a dielectric, an amorphous insulator, a metal with a high melting point or a metal compound with a high melting point as described in Embodiment 1 and its Modification 1. When a dielectric film is used, the mask film  13  with good quality can be formed at a low temperature by employing the ECR sputtering. 
     Furthermore, by using the nitride semiconductor layer including a dislocation low-density region of this embodiment, not only a light emitting device but also another semiconductor device such as an electronic device can be fabricated. Thus, the reliability and the yield of the semiconductor device can be improved. 
     Embodiment 7 
     Embodiment 7 of the invention will now be described with reference to the accompanying drawings. 
       FIG. 32  shows the sectional structure of a gallium nitride-based semiconductor laser diode of Embodiment 7. In  FIG. 32 , like reference numerals are used to refer to like elements shown in  FIG. 1  so as to omit the description. 
     As is shown in  FIG. 32 , the semiconductor laser diode of this embodiment includes convexes  12   a  in the shape of stripes formed in a first formation cycle in an upper portion of the seed layer  12  and serving as the seed crystal for the ELOG, and one ridge  31 A for current injection and plural dummy ridges  31 B for aligning the ridge  31 A formed in an upper portion of the lamination body  30 . The ridge  31 A and the dummy ridges  31 B are arranged in the same direction as the convexes  12   a  in a second formation cycle different from the first formation cycle. 
     Now, a method of fabricating the semiconductor laser diode having the aforementioned structure will be described with reference to the drawings. 
       FIGS. 33 through 35  are sectional views for showing procedures in the method of fabricating the semiconductor laser diode of Embodiment 7. 
     First, as is shown in  FIG. 33 , a seed layer  12  of GaN is grown on a substrate  11  of sapphire by the MOVPE in the same manner as in Embodiment 1, and convexes  12   a  in the shape of ridge stripes are formed in an upper portion of the seed layer  12  by the photolithography and the dry etching using a resist film. In this embodiment, for example, the convex  12   a  has a sectional width of approximately 4 μm, a groove  12   b  has a sectional width of approximately 12 μm, and the first formation cycle is 16 μm. 
     Next, a mask film  13  of silicon nitride is deposited by the ECR sputtering on the entire top face of the seed layer  12  including the convexes  12   a , and the resist film is lifted off, there by exposing at least the top faces of the convexes  12   a  from the mask film  13 . At this point, the mask film  13  may or may not cover the walls of the grooves  12   b.    
     Subsequently, a selectively grown layer  14  and a lamination body  30  are successively grown by the MOVPE on the seed layer  12  by using, as the seed crystal, the C plane appearing on the top faces of the convexes  12   a  not covered with the mask film  13  in the same manner as in Embodiment 1. 
     Next, as is shown in  FIG. 34 , an upper portion of a p-type cladding layer  20  and a p-type contact layer  21  are formed into a ridge  31 A and dummy ridges  31 B each with a sectional width of approximately 3 μm in the second formation cycle of 18 μm. At this point, the ridge  31 A for current injection is formed in a region above a gap  12   c  and not overlapping a junction portion  14   a , namely, in a dislocation low-density region including few crystal dislocations. Thereafter, the side faces of the ridge  31 A and the dummy ridges  31 B and areas therebetween are covered with an insulating film  35  of aluminum nitride (AlN) by the ECR sputtering in an argon atmosphere by using metallic aluminum and nitrogen as material sources. 
     Next, as is shown in  FIG. 35 , faces of the lamination body  30  excluding the ridge  31 A is dry etched, so as to partly expose an n-type contact layer  15  in such a manner that the dummy ridge  31 B can be formed from an n-type cladding layer  16 . Then, an insulating film  22  of silicon nitride is deposited on exposed faces of the lamination body  30 . 
     Then, as is shown in  FIG. 32 , openings are formed in the insulating film  22  in positions on and on both sides of the ridge  31 A and in positions on and on both sides of one dummy ridge  31 B above the n-type contact layer  15  by the reactive ion etching (RIE) using carbon tetrafluoride (CF 4 ). Thereafter, a p-side electrode  23  is formed over exposed portions in the openings of the insulating film  22  on and on the sides of the ridge  31 A, and an n-side electrode  24  is formed over exposed portions in the openings of the insulating film  22  on and on the sides of the dummy ridge  31 B above the n-type contact layer  15 . In removing the portions of the insulating film  22  on and on the sides of the ridge  31 A, the insulating film  35  formed below the insulating film  22  is slightly etched, which is negligible when the current confinement of an injected current and the horizontal lateral mode control are not affected. 
     The semiconductor laser diode fabricated in the aforementioned manner shows laser action at a wavelength of approximately 403 nm owing to a MQW active layer  18  including a well layer of Ga 0.8 In 0.2 N with a thickness of approximately 3 nm and a barrier layer of GaN with a thickness of approximately 6 nm. 
     Now, the alignment of the ridge  31 A and the dummy ridges  31 B against the convexes  12   a , that is, a characteristic of the method of fabricating the semiconductor laser diode of this embodiment, will be described with reference to the drawings. 
     As described above, it is indispensable for improving the characteristic of the semiconductor laser diode to form the ridge  31 A for current injection in the dislocation low-density region of the lamination body  30  in FIG.  32 . 
     FIG.  36 ( a ) shows examples of a ridge  31  appropriate for current injection among plural ridges  31 . Each of the ridges  31  marked with ∘ is formed above a region having the lowest dislocation density between the convex  12   a  and the junction portion  14   a . In contrast, each of the ridges  31  marked with X is formed above a dislocation high-density region. 
     Accordingly, in the etching for partly exposing the n-type contact layer  15  shown in  FIG. 35 , it is necessary to allow the ridge  31  marked with ∘ to remain as the ridge  31 A for current injection. 
     Therefore, in this embodiment, the following method is employed so as to easily and definitely distinguish the ridge  31 A from the dummy ridge  31 B as shown in FIG.  36 ( b ). 
     Each of the ridges is previously given a number or the like for distinguishing the ridge  31 A and the dummy ridges  31 B having the second formation cycle (pattern B). It is herein assumed that the ridge  31  given a number “2” is to be used as the ridge  31 A for current injection. 
     On the other hand, on the wafer, for example, in cleavage areas between the laser diodes on the substrate  11 , alignment marks (alignment pattern) are provided so as to correspond to the respective numbers given to the ridges  31 . In this embodiment, since a difference between the first formation cycle (pattern A) and the second formation cycle (pattern B) is 2 μm, the positional relationship between a ridge  31  and the closest convex  12   a  becomes the same at every 8 cycles of the pattern B. Accordingly, when at least 8 alignment marks are provided, at least one ridge  31  can be marked with ∘ among the ridges  31  numbered “1” through “8”. 
     Accordingly, in the etching shown in  FIG. 35 , when the boundary of the photomask is aligned, for example, in an area between the dummy ridge  31 B numbered “3” and the dummy ridge  31 B numbered “4”, the ridge  31 A for current injection can be allowed to remain. 
     Also, in the etching for forming the openings in the insulating film  22  for forming the p-side electrode  23 , the ridge  31 A numbered with “2” can be easily identified. 
     Since the chip width of the laser diode is approximately 300 through 500 μm, the third cycle of the ridges numbered “1” through “8” appears not once but twice or three times. 
     Furthermore, the effect exhibited in the mask alignment by the gaps  12   c  in the stripe shape formed between the seed layer  12  and the selectively grown layer  14  will now be described. This effect is exhibited because the top faces of the convexes  12   a  formed between the gaps  12   c  in the upper portion of the seed layer  12  are used as the seed crystal for the ELOG. Specifically, in order to select a ridge with few dislocations, it is necessary to identify a dislocation low-density region in the lamination body through observation from the upside with an optical microscope or the like. In this embodiment, as is shown in  FIG. 32 , the refractive index difference of observation light is largely varied owing to the gaps  12   c , the positions of the convexes  12   a  (the dislocation high-density regions) are obvious. Accordingly, a ridge  31  that is a candidate for the ridge  31 A for current injection and is positioned between the convex  12   a  and the junction portion  14   a  can be easily and definitely identified. As a result, the mask alignment in the photolithography is eased, so as to increase the throughput in the photolithography. 
     Although the first formation cycle of the convexes  12   a  and the second formation cycle of the ridges  31  are both constant in this embodiment, these cycles are not necessarily constant as far as the formation cycles are shifted from each other. For example, each formation cycle may form a sequence group satisfying arithmetical series. 
     Furthermore, the insulating film  35  is formed from aluminum nitride and the insulating film  22  is formed from silicon nitride in this embodiment. However, the materials for the insulating films are not limited to them as far as the etch selectivity against the insulating film  35  is sufficiently large in etching the insulating film  22 . For example, the insulating film  35  may be formed from silicon oxide with the insulating film  22  formed from silicon nitride. Also, the insulating film  22  may be etched by wet etching or dry etching. 
     Although the substrate  11  is made from sapphire, for example, silicon carbide, neodymium gallate (NGO), gallium nitride or the like may be used instead. 
     Furthermore, the mask film  13  may be formed from a dielectric such as silicon nitride and silicon oxide by the ECR sputtering, and more preferably, is formed from a metal with a high melting point such as tungsten or its silicide. 
     Although the lift-off method is used for forming the convexes  12   a  in the upper portion of the seed layer  12 , any other method may be employed instead as far as the convexes  12   a  and the grooves  12   b  can be formed. 
     Moreover, the fabrication method of this embodiment using two kinds of cyclic structures having different cycles is applicable to the conventional ELOG or the like.