Abstract:
A nitride-based semiconductor element having excellent element characteristics is obtained by fabricating a nitride-based semiconductor layer having excellent crystallinity without performing extended etching. The nitride-based semiconductor element comprises a mask layer, having a recess portion, formed on a substantially flat upper surface of an underlayer to partially expose the upper surface of the underlayer, a nitride-based semiconductor layer formed on the exposed part of the underlayer and the mask layer while forming a void on the recess portion of the mask layer, and a nitride-based semiconductor element layer, formed on the nitride-based semiconductor layer, having an element region. During laterally growth, strain is relaxed thereby improving crystallinity. The underlayer is formed in a substantially flat shape, thereby avoiding extended etching.

Description:
This application is a Division of Ser. No. 10/084,050 filed Feb. 28, 2002 now U.S. Pat. No. 6,713,845. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a nitride-based semiconductor element and a method of forming a nitride-based semiconductor, and more specifically, it relates to a nitride-based semiconductor element containing a nitride-based semiconductor formed by epitaxial lateral overgrowth and a method of forming a nitride-based semiconductor. 
   2. Description of the Prior Art 
   A technique of growing a nitride-based semiconductor on an underlayer is known in general. For example, a crystal of GaN, which is one of nitride-based semiconductors lattice-matching with only a small number of types of substrates, is grown on a substrate such as a sapphire substrate. In relation to this, generally known is a technique of inserting a buffer layer grown at a low temperature between the substrate and a GaN layer for growing GaN in excellent crystallinity with a small number of crystal defects. 
   Even if the aforementioned low-temperature buffer layer is employed, however, the density of reducible defects is limited and it is difficult to reduce the number of dislocations. To this end, a technique of reducing the number of dislocations by epitaxial lateral overgrowth (ELOG) of GaN is proposed in general. This epitaxial lateral overgrowth is disclosed in Journal of Oyo Denshi Bussei Bunkakai, Vol. 4 (1998), pp. 53 to 58 and 210 to 215, for example. 
     FIG. 29  is a sectional view for illustrating a conventional method of forming a nitride-based semiconductor by epitaxial lateral overgrowth. Referring to  FIG. 29 , a low-temperature buffer layer  102  is first formed on a sapphire substrate  101 , and thereafter a GaN layer  103  for serving as an underlayer is grown on the low-temperature buffer layer  102  in the conventional method of forming a nitride-based semiconductor by epitaxial lateral overgrowth. 
   Then, striped (elongated) mask layers  104  of SiO 2  or the like are formed on prescribed regions of the GaN layer  103 . The mask layers  104  are employed as selective growth masks for epitaxially laterally overgrowing a GaN layer  105  from the GaN layer  103  serving as an underlayer, so that the GaN layer  105  is vertically (upwardly) grown from exposed portions of the GaN layer  103  and thereafter laterally grown on the mask layers  104 . Dislocations extending in the c-axis direction are laterally bent due to this lateral overgrowth, not to reach a portion around the upper surface of the GaN layer  105 . Thus, the number of dislocations reaching the flat upper surface of the finally formed GaN layer  105  is remarkably reduced as compared with the GaN layer  103  forming the underlayer. 
   In the conventional method of forming a nitride-based semiconductor by epitaxial lateral overgrowth shown in  FIG. 29 , however, the c-axis of the overgrowth region of GaN layer  105  is disadvantageously inclined from the normal direction of the substrate although the number of dislocations resulting from epitaxial lateral overgrowth can be reduced in the GaN layer  105 . In other words, the growth layer of the GaN layer  105  laterally grown on the mask layers  104  is strained due to stress applied thereto. Therefore, the c-axis perpendicular to the sapphire substrate  101  is disadvantageously inclined by about 2° at the maximum as shown by arrows in  FIG. 29 . When the c-axis is displaced, crystallinity is deteriorated to result in inferior element characteristics. 
   In order to suppress such inclination of the c-axis, therefore, a method shown in  FIG. 30  is proposed in general. Referring to  FIG. 30 , a GaN layer  113  serving as an underlayer is formed on a sapphire substrate  111  through a low-temperature buffer layer  112  in this proposed method. Recess portions are formed on the surface of the GaN layer  113  for thereafter forming mask layers  114  having recess portions  114   a  of SiO 2  or the like in recess portions  113   a  of the surface. The mask layers  114  are employed as selective growth masks for epitaxially laterally overgrowing a GaN layer  115  on projection portions of the GaN layer  113  serving as an underlayer. In this case, voids  120  are defined between the mask layers  114  and the epitaxially laterally overgrown GaN layer  115 , thereby reducing the contact areas between the GaN layer  115  and the mask layers  114  when the GaN layer  115  is laterally grown on the mask layers  114 . Thus, stress is hardly applied to the GaN layer  115  laterally grown on the mask layers  114 , and hence strain of the GaN layer  115  is relaxed. Consequently, inclination of the c-axis can be relaxed as compared with the prior art shown in  FIG. 29 , as shown by arrows in  FIG. 30 . 
   In the conventional proposed method shown in  FIG. 30 , however, it is necessary to etch the GaN layer  113  serving as an underlayer for forming the recess portions thereof. In this case, a long time is required for etching the GaN layer  113 , disadvantageously leading to a long process time. 
   In the conventional proposed method shown in  FIG. 30 , most dislocations  116  are bent in intermediate portions during lateral growth of the GaN layer  115  not to reach the surface, as shown in  FIG. 31 . However, some of dislocations  116  are not bent but reach the surface as such. In the conventional proposed method, therefore, it is difficult to further reduce the number of dislocations. 
   SUMMARY OF THE INVENTION 
   An object of the present invention is to provide a nitride-based semiconductor element having excellent device characteristics by obtaining a nitride-based semiconductor layer having excellent crystallinity without performing a long-time etching process. 
   Another object of the present invention is to reduce the number of dislocations in an epitaxially laterally overgrown nitride-based semiconductor layer in the aforementioned nitride-based semiconductor element. 
   Still another object of the present invention is to provide a method of forming a nitride-based semiconductor capable of readily forming a nitride-based semiconductor layer having excellent crystallinity without performing a long-time etching process. 
   A further object of the present invention is to more effectively reduce the number of dislocations reaching the surface of the nitride-based semiconductor in the aforementioned method of forming a nitride-based semiconductor. 
   A nitride-based semiconductor element according to a first aspect of the present invention comprises a mask layer, having a recess portion on the upper surface of the mask layer, formed on a substantially flat upper surface of an underlayer to partially expose the upper surface of the underlayer, a nitride-based semiconductor layer formed on the exposed part of the underlayer and the mask layer while forming a void on the recess portions of the mask layer, and a nitride-based semiconductor element layer, formed on the nitride-based semiconductor layer, having an element region. 
   In the nitride-based semiconductor element according to the first aspect, the mask layer having a recess portion is formed on the substantially flat upper surface of the underlayer as hereinabove described, whereby the nitride-based semiconductor layer is formed with the void on the recess portion of the mask layer when laterally grown on the mask layer. This void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. Further, the underlayer is formed in a substantially flat shape, whereby no etching may be performed over a long time for forming recess portions on the surface of the underlayer consisting of a nitride-based semiconductor or the like, dissimilarly to the prior art. Therefore, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed without performing an etching process for a long time. Consequently, a nitride-based semiconductor layer having excellent crystallinity can be obtained without performing a long-time etching process. When the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having excellent crystallinity, a nitride-based semiconductor element having excellent element characteristics can be obtained. 
   In the aforementioned nitride-based semiconductor element according to the first aspect, the recess portion of the mask layer preferably includes a dent provided on at least part of the upper surface of the mask layer. According to this structure, the void can be readily formed on the mask layer due to the dent when the nitride-based semiconductor layer is laterally grown on the mask layer. 
   In the aforementioned nitride-based semiconductor element according to the first aspect, the recess portion of the mask layer preferably includes a concavely curved upper surface of the mask layer. According to this structure, the void can be readily formed on the mask layer due to the concavely curved upper surface of the mask layer. In this case, the mask layer preferably has an overhanging shape, and the upper surface of the overhanging mask layer is preferably concavely curved. In this case, further, the overhanging mask layer preferably includes a first insulator film formed on the underlayer and a second insulator film, formed on the first insulator film, having a smaller etching rate than the first insulator film. According to this structure, the overhanging mask layer having a laterally protruding second insulator film can be readily obtained by forming the first and second insulator films and thereafter etching the second and first insulator films. 
   In the aforementioned nitride-based semiconductor element according to the first aspect, the underlayer preferably includes a substrate, and the mask layer is preferably formed to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced due to absence of the underlayer. 
   A nitride-based semiconductor element according to a second aspect of the present invention comprises a mask layer, having a recess portion on the upper surface of the mask layer, formed on projection portions of an underlayer having the projection portions on an upper surface to partially expose the upper surface of the underlayer, a nitride-based semiconductor layer formed on the exposed part of the underlayer and the mask layer while forming a void on the recess portion of the mask layer, and a nitride-based semiconductor element layer, formed on the nitride-based semiconductor layer, having an element region. 
   In the nitride-based semiconductor element according to the second aspect, the mask layer having a recess portion is formed on the upper surface of the underlayer as hereinabove described, whereby the nitride-based semiconductor layer is formed with the void on the recess portion of the mask layer when laterally grown on the mask layer. This void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. When the recess portions are formed on the underlayer and the mask layer is formed on projection portions thereof to have an overhanging shape, raw material is hardly supplied to a portion located under the overhang of the mask layer, to result in difference in growth rate between the portion located under the overhang and the remaining portions. Thus, lateral growth is dominant in the portion located under the overhang having a low growth rate from an extremely initial stage, whereby dislocations start to laterally bend from the initial stage. Consequently, it is possible to more effectively prevent the dislocations from reaching the surface of the nitride-based semiconductor layer. Therefore, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed while further reducing the number of dislocations. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be obtained. When the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having more excellent crystallinity, a nitride-based semiconductor element having more excellent element characteristics can be obtained. 
   In the aforementioned nitride-based semiconductor element according to the second aspect, the recess portion of the mask layer preferably includes a dent provided on at least part of the upper surface of the mask layer. According to this structure, the void can be readily formed on the mask layer due to the dent when the nitride-based semiconductor layer is laterally grown on the mask layer. 
   In the aforementioned nitride-based semiconductor element according to the second aspect, the recess portion of the mask layer preferably includes a concavely curved upper surface of the mask layer. According to this structure, the void can be readily formed on the mask layer due to the concavely curved surface of the mask layer. In this case, the mask layer preferably has an overhanging shape, and the upper surface of the overhanging mask layer is preferably concavely curved. 
   In the aforementioned nitride-based semiconductor element according to the second aspect, the underlayer preferably includes a substrate, and the mask layer is preferably formed to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced due to absence of the underlayer. 
   A method of forming a nitride-based semiconductor according to a third aspect of the present invention comprises steps of forming a mask layer, having a recess portion on the upper surface of the mask layer on a substantially flat upper surface of an underlayer to partially expose the upper surface of the underlayer, and growing a nitride-based semiconductor layer on the exposed part of the underlayer and the mask layer. 
   In the method of forming a nitride-based semiconductor according to the third aspect, the mask layer having a recess portion is formed as hereinabove described, whereby the nitride-based semiconductor layer is formed with the void on the recess portion of the mask layer when laterally grown on the mask layer. The void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. The underlayer is formed in a substantially flat shape, whereby no etching may be performed over a long time for forming recess portions on the underlayer consisting of a nitride-based semiconductor or the like, dissimilarly to the prior art. Thus, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed without performing an etching process for a long time. Consequently, a nitride-based semiconductor layer having excellent crystallinity can be readily formed without performing a long-time etching process. 
   In the aforementioned method of forming a nitride-based semiconductor according to the third aspect, the step of forming the mask layer preferably includes a step of forming the mask layer on a prescribed region of the underlayer and thereafter partially etching the upper surface of the mask layer thereby forming the recess portion on the upper surface of the mask layer. According to this structure, the mask layer having the recess portion on the upper surface can be readily formed. 
   In the aforementioned method of forming a nitride-based semiconductor according to the third aspect, the step of forming the mask layer preferably includes steps of forming a first mask material layer on part of a region of the underlayer formed with the mask layer, forming a second mask material layer to cover the first mask material layer and the underlayer, and etching the second mask material layer while leaving the first mask material layer thereby forming the mask layer consisting of the first mask material layer and the second mask material layer and having the recess portion on the upper surface. According to this structure, the mask layer having the recess portion on the upper surface can be readily formed. 
   In the aforementioned method of forming a nitride-based semiconductor according to the third aspect, the underlayer preferably includes a substrate, and the step of forming the mask layer preferably includes a step of forming the mask layer to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced due to absence of the underlayer. 
   The aforementioned method of forming a nitride-based semiconductor according to the third aspect preferably further comprises a step of growing a nitride-based semiconductor element layer having an element region on the nitride-based semiconductor layer. According to this structure, the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having excellent crystallinity, whereby a nitride-based semiconductor element having excellent element characteristics can be readily formed. 
   A method of forming a nitride-based semiconductor according to a fourth aspect of the present invention comprises steps of forming a mask layer, having a recess portion on the upper surface of the mask layer on projection portions of an underlayer having the projection portions on upper surface for partially exposing the surface of the underlayer, and growing a nitride-based semiconductor layer on the exposed part of the underlayer and the mask layer. 
   In the method of forming a nitride-based semiconductor according to the fourth aspect, the mask layer having a recess portion is formed on the upper surface of the underlayer, whereby the nitride-based semiconductor layer is formed while a void remaining on the recess portion of the mask layer when laterally grown on the mask layer. This void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. When the projection portion is formed on the underlayer and the mask layer is formed on the projection portions thereof to have an overhanging shape, raw material is hardly supplied to a portion located under the overhang of the mask layer, inducing difference in growth rate between the portion located under the overhang and the remaining portions. Thus, lateral growth is dominant in the portion located under the overhang having a low growth rate from an extremely initial stage, whereby dislocations start to laterally bend from the initial stage. Consequently, it is possible to more effectively prevent the dislocations from reaching the surface of the nitride-based semiconductor layer. Therefore, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed while further reducing the number of dislocations. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be obtained. 
   In the aforementioned method of forming a nitride-based semiconductor according to the fourth aspect, the underlayer preferably includes a substrate, and the step of forming the mask layer preferably includes a step of forming the mask layer to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced-due to absence of the underlayer. 
   The aforementioned method of forming a nitride-based semiconductor according to the fourth aspect preferably further comprises a step of growing a nitride-based semiconductor element layer having an element region on the nitride-based semiconductor layer. According to this structure, the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having excellent crystallinity, whereby a nitride-based semiconductor element having excellent element characteristics can be readily formed. 
   A method of forming a nitride-based semiconductor according to a fifth aspect of the present invention comprises steps of forming a mask layer having an overhanging shape on a substantially flat upper surface of an underlayer to expose part of the flat upper surface of the underlayer, and growing a nitride-based semiconductor layer on the exposed part of the underlayer and the mask layer. 
   In the method of forming a nitride-based semiconductor according to the fifth aspect, the overhanging mask layer is formed as hereinabove described, whereby the nitride-based semiconductor layer applies upward force to the protrusion of the overhanging mask layer in the process of growth, for curving the upper surface of the overhanging mask layer and defining a dent. Thus, the nitride-based semiconductor layer is formed while forming a void on the upper surface of the curved dent of the mask layer. This void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. In this case, the curved dent of the mask layer reduces the contact area between the upper surface of the mask layer and the growth layer, whereby inclination of the c-axis can be reduced to substantially 0°. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be readily formed. When the underlayer is formed in a substantially flat shape, no etching may be performed over a long time for forming recess portions on the underlayer consisting of a nitride-based semiconductor or the like, dissimilarly to the prior art. Therefore, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed without performing an etching process over a long time. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be readily formed without performing a long-time etching process. 
   According to the fifth aspect, the step of growing the nitride-based semiconductor layer preferably includes a step of growing the nitride-based semiconductor layer from under the mask layer having an overhanging shape and applying force from under the overhang of the mask layer thereby curving the upper surface of the overhanging mask layer. According to this structure, the upper surface is curved to define a dent, whereby the nitride-based semiconductor layer can be readily formed while forming a void on the dent of the mask layer. 
   According to the fifth aspect, the step of forming the mask layer preferably includes steps of forming a first mask material layer on the underlayer while forming a second mask material layer having a smaller etching rate than the first mask material layer on the first mask material layer, and etching the first mask material layer and the second mask material layer thereby forming the overhanging mask layer having the first mask material layer and the second mask material layer. According to this structure, the overhanging mask layer can be readily formed. 
   In the aforementioned method of forming a nitride-based semiconductor according to the fifth aspect, the underlayer preferably includes a substrate, and the step of forming the mask layer preferably includes a step of forming the mask layer to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced due to absence of the underlayer. 
   The aforementioned method of forming a nitride-based semiconductor according to the fifth aspect preferably further comprises a step of growing a nitride-based semiconductor element layer having an element region on the nitride-based semiconductor layer. According to this structure, the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having excellent crystallinity, whereby a nitride-based semiconductor element having excellent element characteristics can be readily formed. 
   A method of forming a nitride-based semiconductor according to a sixth aspect of the present invention comprises steps of forming a mask layer, having an overhanging shape on projection portions of an upper surface of an underlayer having the projection portions to expose part of the upper surface of the underlayer, and growing a nitride-based semiconductor layer on the exposed part of the underlayer and the mask layer. 
   In the method of forming a nitride-based semiconductor according to the sixth aspect, the overhanging mask layer is formed as hereinabove described, whereby the nitride-based semiconductor layer applies upward force to the protrusion of the overhanging mask layer in the process of growth, for curving the upper surface of the overhanging mask layer and forming concavely curved surface. Thus, the nitride-based semiconductor layer is formed while forming a void on the upper surface of the curved dent of the mask layer. This void relaxes strain of the laterally grown nitride-based semiconductor layer, whereby inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed. In this case, the curved dent of the mask layer reduces the contact area between the upper surface of the mask layer and the growth layer, whereby inclination of the c-axis can be reduced to substantially 0°. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be readily formed. When the underlayer is formed on projection portions and the mask layer is formed on projection portions thereof to have an overhanging shape, raw material is hardly supplied to a portion located under the overhang of the mask layer, to result in difference in growth rate between the portion located under the overhang and the remaining portions. Thus, lateral growth is dominant in the portion located under the overhang having a low growth rate from an extremely initial stage, whereby dislocations start to laterally bend from the initial stage. Consequently, it is possible to more effectively prevent the dislocations from reaching the surface of the nitride-based semiconductor layer. Therefore, inclination of the c-axis (crystal axis) of the nitride-based semiconductor layer can be suppressed while further reducing the number of dislocations. Consequently, a nitride-based semiconductor layer having more excellent crystallinity can be obtained. 
   According to the aforementioned sixth aspect, the step of growing the nitride-based semiconductor layer preferably includes a step of growing the nitride-based semiconductor layer from under the mask layer having an overhanging shape and applying force from under the overhang of the mask layer thereby curving the upper surface of the overhanging mask layer. According to this structure, the upper surface is curved to define a dent, whereby the nitride-based semiconductor layer can be readily formed while forming a void on the dent of the mask layer. 
   In the aforementioned method of forming a nitride-based semiconductor according to the sixth aspect, the underlayer preferably includes a substrate, and the step of forming the mask layer preferably includes a step of forming the mask layer to be in contact with the upper surface of the substrate. According to this structure, no underlayer may be formed on the substrate, whereby the fabrication process can be simplified. Further, the total thickness can be reduced due to absence of the underlayer. 
   The aforementioned method of forming a nitride-based semiconductor according to the sixth aspect preferably further comprises a step of growing a nitride-based semiconductor element layer having an element region on the nitride-based semiconductor layer. According to this structure, the nitride-based semiconductor element layer having an element region is grown on the nitride-based semiconductor layer having excellent crystallinity, whereby a nitride-based semiconductor element having excellent element characteristics can be readily formed. 
   The foregoing and other objects, features, aspects and advantages of the present invention will become more apparent from the following detailed description of the present invention when taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIGS. 1 to 4  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a first embodiment of the present invention; 
       FIG. 5  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the first embodiment of the present invention; 
       FIGS. 6 to 10  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a second embodiment of the present invention; 
       FIG. 11  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the second embodiment of the present invention; 
       FIGS. 12 to 14  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a third embodiment of the present invention; 
       FIG. 15  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the third embodiment of the present invention; 
       FIGS. 16 to 18  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a fourth embodiment of the present invention; 
       FIG. 19  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the fourth embodiment of the present invention; 
       FIGS. 20 to 22  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a fifth embodiment of the present invention; 
       FIG. 23  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the fifth embodiment of the present invention; 
       FIGS. 24 to 27  are sectional views for illustrating a method of forming a nitride-based semiconductor according to a sixth embodiment of the present invention; 
       FIG. 28  is a sectional view showing a semiconductor laser device fabricated with the method of forming a nitride-based semiconductor according to the sixth embodiment of the present invention; 
       FIG. 29  is a sectional view for illustrating a conventional method of forming a nitride-based semiconductor; 
       FIG. 30  is a sectional view for illustrating a conventional proposed method of forming a nitride-based semiconductor; and 
       FIG. 31  is a sectional view for illustrating a problem in the conventional proposed method of forming a nitride-based semiconductor shown in  FIG. 30 . 
   

   DESCRIPTION OF THE PREFERRED EMBODIMENTS 
   Embodiments of the present invention are now described with reference to the drawings. 
   (First Embodiment) 
   A method of forming a nitride-based semiconductor according to a first embodiment of the present invention is described with reference to  FIGS. 1 to 4 . 
   First, a low-temperature buffer layer  2  of GaN or AlGaN is grown on a sapphire substrate  1  by MOCVD (metal organic chemical vapor deposition) or HVPE (hydride vapor phase epitaxy) in a thickness of about 20 nm to about 30 nm, as shown in  FIG. 1 . An undoped GaN layer  3  of at least about 2 μm in thickness for serving as an underlayer is grown on the low-temperature buffer layer  2  by MOCVD or HVPE. A mask layer  4  of SiO 2  or SiN is formed on the undoped GaN layer  3 . Resist films  7  are formed on prescribed regions of the mask layer  4 . The resist films  7  are employed as masks for etching the mask layer  4 , thereby forming patterned striped (elongated) mask layers  4  as shown in  FIG. 2 . The striped mask layers  4  are formed to have a cycle of about 10 μm. Thereafter the resist films  7  are removed. 
   Then, resist films  8  are formed to cover ends of the mask layers  4  and exposed parts of the undoped GaN layer  3 , as shown in  FIG. 3 . The resist films  8  are employed as masks for partially etching the upper surfaces of the mask layers  4 , thereby forming recess portions  4   a  on the centers of the upper surfaces of the mask layers  4 . The recess portions  4   a  are so formed that the mask layers  4  are about 6 μm in width and the recess portions  4   a  are about 4 μm in width. Further, the mask layers  4  are so etched that the ends thereof are about 0.5 μm in thickness and the parts formed with the recess portions  4   a  are about 0.2 μm to about 0.3 μm in thickness. Thereafter the resist films  8  are removed. 
   Then, the mask layers  4  having the recess portions  4   a  are employed as selective growth masks for epitaxially laterally overgrowing an undoped GaN layer  5  on the undoped GaN layer  3  and the mask layers  4 , as shown in  FIG. 4 . The undoped GaN layer  5  having a flat upper surface is formed while forming voids  6  on the recess portions  4   a  of the mask layers  4 . 
   According to the first embodiment, as hereinabove described, the mask layers  4  having the recess portions  4   a  are formed on the flat upper surface of the undoped GaN layer  3  serving as an underlayer, whereby the undoped GaN layer  5  is formed wile forming the voids  6  on the recess portions  4   a  of the mask layers  4  when laterally grown on the mask layers  4 . The voids  6  relax strain of the undoped GaN layer  5  laterally grown on the mask layers  4 , whereby inclination of the c-axis (crystal axis) of the undoped GaN layer  5  can be suppressed. According to the first embodiment, inclination of the c-axis of the undoped GaN layer  5  can be reduced to not more than about 0.1°. 
   The undoped GaN layer  3  serving as an underlayer has a flat shape, whereby no etching may be performed over a long time for forming recess portion dissimilarly to the conventional proposed structure shown in  FIG. 30 . Therefore, inclination of the c-axis (crystal axis) of the epitaxially laterally overgrown undoped GaN layer  5  can be suppressed without performing an etching process over a long time. Consequently, the undoped GaN layer  5  having excellent crystallinity can be readily formed without performing a long-time etching process. 
     FIG. 5  is a sectional view of a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the first embodiment. Referring to  FIG. 5 , an n-type GaN contact layer  11 , doped with Si, having a thickness of about 5 μm is formed on the undoped GaN layer  5  shown in  FIG. 4  in the semiconductor laser device according to the first embodiment. An n-type In 0.1 Ga 0.9 N anti-cracking layer  12 , doped with Si, having a thickness of about 0.1 μm is formed on the n-type GaN contact layer  11 . An n-type Al 0.08 Ga 0.92 N cladding layer  13 , doped with Si, having a thickness of about 1 μm is formed on the n-type In 0.1 Ga 0.9 N anti-cracking layer  12 . An MQW emission layer  14  having a quantum well structure is formed on the n-type Al 0.08 Ga 0.92 N cladding layer  13 . 
   The MQW emission layer  14  includes a GaN guide layer, doped with Si, having a thickness of about 0.1 μm, an In 0.03 Ga 0.97 N barrier layer, doped with Si, having a thickness of about 6 nm, an In 0.10 Ga 0.90 N well layer, doped with Si, having a thickness of about 3 nm, an In 0.03 Ga 0.97 N barrier layer, doped with Si, having a thickness of about 6 nm, an In 0.10 Ga 0.90 N well layer, doped with Si, having a thickness of about 3 nm, an In 0.03 Ga 0.97 N barrier layer, doped with Si, having a thickness of about 6 nm, an In 0.10 Ga 0.90 N well layer, doped with Si, having a thickness of about 3 nm, an In 0.03 Ga 0.97 N barrier layer, doped with Si, having a thickness of about 6 nm, an Al 0.2 Ga 0.8 N cap layer, doped with Mg, having a thickness of about 2 nm and a GaN guide layer, doped with Mg, having a thickness of about 0.1 μm successively stacked from the side of the substrate  1 . 
   A p-type Al 0.08 Ga 0.92 N cladding layer  15 , doped with Mg, having a thickness of about 0.4 μm is formed on the MQW emission layer  14 . A p-type GaN contact layer  16 , doped with Mg, having a thickness of about 0.1 μm is formed on the p-type Al 0.08 Ga 0.92 N cladding layer  15 . A p-side electrode  17  is formed on the p-type GaN contact layer  16 . An n-side electrode  18  is formed on an exposed surface of the n-type GaN contact layer  11 . Protective films  19  consisting of an insulator are formed to cover the side surfaces and the upper surfaces of the layers  11  to  16 . 
   The aforementioned layers  11  to  16  are examples of the “nitride-based semiconductor element layer” according to the present invention. 
   In the aforementioned semiconductor laser device according to the first embodiment, the layers  11  to  16  are formed on the undoped GaN layer  5  reduced in inclination of the c-axis, formed by the method shown in  FIGS. 1 to 4  without a long-time etching process, whereby excellent crystallinity can be implemented in the layers  11  to  16 . According to the first embodiment, therefore, a semiconductor laser device having excellent device characteristics can be obtained without performing a long-time etching process. 
   (Second Embodiment) 
   Referring to  FIGS. 6 to 10 , a second embodiment of the present invention is described with reference to a method of directly epitaxially laterally overgrowing a nitride-based semiconductor layer on a substrate through mask layers having recess portions. The method according to the second embodiment is now described in detail. 
   First, a first mask material layer  22   b  consisting of SiO 2  or SiN is formed on a sapphire substrate  21  in a thickness of about 0.2 μm to about 0.3 μm, as shown in  FIG. 6 . Resist films  26  are formed on prescribed regions of the first mask material layer  22   b . The resist films  26  are employed as masks for etching the first mask material layer  22   b , thereby forming patterned first mask material layers  22   b  as shown in  FIG. 7 . Thereafter the resist films  26  are removed. 
   Then, a second mask material layer  22   c  of SiO 2  or SiN having a thickness of about 0.2 μm to about 0.3 μm is formed to cover the first mask material layers  22   b  and exposed parts of the sapphire substrate  21 , as shown in  FIG. 8 . Thus, recess portions  22   a  are formed on the surface of the second mask material layer  22   c . Resist films  27  are formed to cover the recess portions  22   a  and portions close to both ends of the recess portions  22   a . The resist films  27  are employed as masks for etching the second mask material layer  22   c , thereby forming mask layers  22  consisting of the patterned first and second mask material layers  22   b  and  22   c , as shown in  FIG. 9 . The recess portions  22   a  are formed on the upper surfaces of the mask layers  22 . The mask layers  22  are formed to have a width of about 6 μm, an end thickness of about 0.5 μm and a central thickness of about 0.2 μm to about 0.3 μm with the recess portions  22   a  of about 4 μm in width. The mask layers  22  are formed in a striped manner to have a cycle of about 10 μm. Thereafter the resist films  27  are removed. 
   Then, low-temperature buffer layers  23  of GaN having a thickness of about 20 nm to about 30 nm are grown on exposed parts of the sapphire substrate  21  by MOCVD or HVPE located between the mask layers  22 , as shown in  FIG. 10 . Thereafter an undoped GaN layer  24  is epitaxially laterally overgrown on the low-temperature buffer layers  23  and the mask layers  22 , to have a flat upper surface. In this case, voids  25  are formed on the recess portions  22   a  of the mask layers  22 . The voids  25  relax strain of the laterally grown undoped GaN layer  24  also in the second embodiment, whereby inclination of the c-axis (crystal axis) of the undoped GaN layer  24  can be reduced to not more than about 0.1°. The sapphire substrate  21  serving as an underlayer has a flat shape, whereby no etching process may be performed over a long time for forming recess portions on the GaN layer  24 , dissimilarly to the prior art shown in  FIG. 30 . Therefore, inclination of the c-axis (crystal axis) of the undoped GaN layer  24  can be suppressed without performing a long-time etching process. Consequently, the undoped GaN layer  24  having excellent crystallinity can be obtained with no long-time etching process. 
   According to the second embodiment, the undoped GaN layer  24  is epitaxially laterally overgrown on the sapphire substrate  21 , whereby no GaN layer for serving as an underlayer may be provided dissimilarly to the first embodiment. Therefore, the fabrication process can be more simplified as compared with the first embodiment. 
     FIG. 11  is a sectional view showing a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the second embodiment. Referring to  FIG. 11 , layers  11  to  16 , electrodes  17  and  18  and protective films  19  similar to those of the first embodiment shown in  FIG. 5  are formed on the undoped layer  24  shown in  FIG. 10  in the second embodiment. 
   In the semiconductor laser device according to the second embodiment, the layers  11  to  16  are formed on the undoped GaN layer  24  reduced in inclination of the c-axis formed by the method according to the second embodiment shown in  FIGS. 7 to 10  with no long-time etching process, whereby excellent crystallinity can be implemented in the layers  11  to  16 . According to the second embodiment, therefore, a semiconductor laser device having excellent device characteristics can be obtained with no long-time etching process, similarly to the first embodiment. 
   (Third Embodiment) 
   A method of forming a nitride-based semiconductor according to a third embodiment of the present invention is now described with reference to  FIGS. 12 to 14 . 
   First, a low-temperature buffer layer  32  of GaN or AlGaN having a thickness of about 20 nm to about 30 nm is grown on a sapphire substrate  31  by MOCVD or HVPE, as shown in  FIG. 12 . An undoped GaN layer  33  for serving as an underlayer is grown on the low-temperature buffer layer  32  by MOCVB or HVPE in a thickness of at least about 2 μm. A first mask material layer  34   b  of SiN having a thickness of about 0.05 μm is formed on the undoped GaN layer  33  by plasma CVD with RF power of 125 W. A second mask material layer  34   c  of SiN having a thickness of about 0.45 μm is formed on the first mask material layer  34   b  by plasma CVD with RF power of 250 W. Resist films  37  are formed on prescribed regions of the second mask material layer  34   c.    
   The resist films  37  are employed as masks for wet-etching the second mask material layer  34   c  and the first mask material layer  34   b  with buffered hydrofluoric acid. In this case, the first mask material layer  34   b  formed under the aforementioned conditions is easier to etch as compared with the second mask material layer  34   c . When the resist films  37  are employed as masks for over-etching the second mask material layer  34   c  and the first mask material layer  34   b , therefore, striped mask layers  34  consisting of the first and second mask material layers  34   b  and  34   c  having an overhanging shape are formed as shown in  FIG. 13 . The striped mask layers  34  are formed to have a cycle of about 7 μm. Thereafter the resist films  37  are removed. 
   Then, the mask layers  34  are employed as selective growth masks for epitaxially laterally overgrowing an undoped GaN layer  35  on the undoped GaN layer  33  serving as an underlayer to have a flat upper surface, as shown in  FIG. 14 . 
   When the undoped GaN layer  35  is epitaxially laterally overgrown on the undoped GaN layer  33  serving as an underlayer in the third embodiment, the undoped GaN layer  35  applies upward force to protrusions (overhangs) of the overhanging mask layers  34  in the process of growth, thereby curving the upper surfaces of the overhanging mask layers  34 . Thus, dents  34   a  are formed on the upper surfaces of the mask layers  34 . When the undoped GaN layer  35  is continuously grown on the dents  34   a , voids  36  are formed on the dents  34   a.    
   The voids  36  relax strain of the laterally grown undoped GaN layer  35 , whereby inclination of the c-axis (crystal axis) of the undoped GaN layer  35  can be suppressed. Particularly when the mask layers  34  are curved to form the dents  34   a  as in the third embodiment, the contact areas between the upper surfaces of the mask layers  34  and the grown undoped GaN layer  35  are more reduced as compared with aforementioned first and second embodiments, whereby inclination of the c-axis can be reduced substantially to 0°. Thus, according to the third embodiment, the undoped GaN layer  35  can be formed with superior crystallinity to those in the first and second embodiments. 
   According to the third embodiment, the undoped GaN layer  33  serving as an underlayer has a flat upper surface similarly to the aforementioned first embodiment, whereby no etching process may be performed over a long time for forming recess portions on the surface of the underlayer consisting of GaN dissimilarly to the prior art shown in  FIG. 30 . Consequently, inclination of the c-axis (crystal axis) of the undoped GaN layer  35  can be suppressed without performing a long-time etching process. Thus, the undoped GaN layer  35  having superior crystallinity can be readily formed with no long-time etching process. 
     FIG. 15  is a sectional view showing a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the third embodiment. Referring to  FIG. 15 , layers  11  to  16 , electrodes  17  and  18  and protective films  19  similar to those of the first embodiment shown in  FIG. 5  are formed on the undoped GaN layer  35  shown in  FIG. 14  in the semiconductor laser device according to the third embodiment. Thus, the layers  11  to  16  are formed on the undoped GaN layer  35  hardly having inclination of the c-axis formed by the method shown in  FIGS. 12 to 14  with no long-time etching process in the semiconductor laser device according to the third embodiment, whereby superior crystallinity can be implemented in the layers  11  to  16 . Consequently, a semiconductor laser device having superior device characteristics can be obtained with no long-time etching process. 
   (Fourth Embodiment) 
   Referring to  FIGS. 16 to 18 , a fourth embodiment of the present invention is described with reference to an example of directly epitaxially laterally overgrowing a nitride-based semiconductor layer on a substrate without employing an underlayer dissimilarly to the aforementioned third embodiment. 
   First, overhanging mask layers  42  consisting of first mask material layers  42   b  of SiN, formed by plasma CVD with RF power of 125 W, having a thickness of about 0.05 μm and second mask material layers  42   c  of SiN, formed by plasma CVD with RF power of 250 W, having a thickness of about 0.45 μm are formed on a sapphire substrate  41  through a process similar to that of the third embodiment shown in  FIGS. 12 and 13 , as shown in  FIG. 16 . The overhanging mask layers  42  are formed in the shape of stripes having a cycle of about 7 μm. 
   Then, low-temperature buffer layers  43  of GaN are grown on exposed parts of the sapphire substrate  41  by MOCVD or HVPE located between the mask layers  42  in a thickness of about 20 nm to about 30 nm, as shown in  FIG. 17 . In this state, the upper surfaces of the overhanging mask layers  42  are not curved. 
   Then, the overhanging mask layers  42  are employed as selective growth masks for epitaxially laterally overgrowing an undoped GaN layer  44  on the low-temperature buffer layers  43  and the mask layers  42  by MOCVD or HVPE, as shown in  FIG. 18 . In this case, the undoped GaN layer  44  grown under protrusions (overhangs) of the mask layers  42  apply upward force to the overhangs of the mask layers  42 , whereby the upper surfaces of the mask layers  42  are curved to form dents  42   a . When the undoped GaN layer  44  is further grown on the dents  42   a , the undoped GaN layer  44  has a flat upper surface while forming voids  45  on the dents  42   a.    
   The voids  45  relax strain of the laterally grown undoped GaN layer  44 , whereby inclination of the c-axis (crystal axis) of the undoped GaN layer  44  can be suppressed. Particularly in the fourth embodiment, the mask layers  42  are curved to form the dents  42   a  similarly to the third embodiment, whereby the contact areas between the upper surfaces of the mask layers  42  and the grown undoped GaN layer  44  are more reduced as compared with the aforementioned first and second embodiments. Thus, inclination of the c-axis can be reduced substantially to 0°. Consequently, the undoped GaN layer  44  can be formed with superior crystallinity to those in the first and second embodiments according to the fourth embodiment. 
   According to the fourth embodiment, further, the sapphire substrate  41  serving as an underlayer has a flat shape, whereby no etching process may be performed over a long time for forming recess portions on the surface of the GaN layer serving as an dissimilarly to the prior art shown in  FIG. 30 . According to the fourth embodiment, therefore, inclination of the c-axis (crystal axis) of the undoped GaN layer  44  can be reduced to substantially 0° without performing a long-time etching process, similarly to the third embodiment. Consequently, the undoped GaN layer  44  having superior crystallinity can be formed with no long-time etching process. 
   According to the fourth embodiment, further, the undoped GaN layer  44  is directly epitaxially laterally overgrown on the sapphire substrate  41  through the low-temperature buffer layer  43  without employing an underlayer of GaN dissimilarly to the aforementioned third embodiment, whereby no GaN underlayer may be provided. According to the fourth embodiment, therefore, the fabrication process can be more simplified as compared with the third embodiment. 
     FIG. 19  is a sectional view showing a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the fourth embodiment. Referring to  FIG. 19 , layers  11  to  16 , electrodes  17  and  18  and protective films  19  similar to those of the first embodiment shown in  FIG. 5  are formed on the undoped GaN layer  44  shown in  FIG. 18  in the semiconductor laser device according to the fourth embodiment. The layers  11  to  16  are formed on the undoped GaN layer  44  suppressed to substantially 0° in inclination of the c-axis formed by the method shown in  FIGS. 16 to 18  with no long-time etching process in the semiconductor laser device according to the fourth embodiment, whereby superior crystallinity can be implemented in the layers  11  to  16 . Consequently, a semiconductor laser device having superior device characteristics can be obtained with no long-time etching process according to the fourth embodiment, similarly to the third embodiment. 
   (Fifth Embodiment) 
   A method of forming a nitride-based semiconductor according to a fifth embodiment of the present invention is now described with reference to  FIGS. 20 to 22 . 
   First, a low-temperature buffer layer  52  of GaN or AlGaN is grown on a sapphire substrate  51  by MOCVD or HVPE in a thickness of about 20 nm to about 30 nm, as shown in  FIG. 20 . An undoped GaN layer  53  for serving as an underlayer is grown on the low-temperature buffer layer  52  by MOCVD or HVPE in a thickness of at least about 2 μm. Thereafter mask layers  54  of SiN or SiO 2  are formed on prescribed regions of the upper surface of the undoped GaN layer  53  in a thickness of about 0.2 μm and a width of about 4 μm. The mask layers  54  are formed in the shape of stripes to have a cycle of about 7 μm. The mask layers  54  are employed as masks for wet-etching the undoped GaN layer  53  serving as an underlayer, thereby forming recess portions  53   a  on the undoped GaN layer  53 . The recess portions  53   a  are formed by etching the undoped GaN layer  53  until regions of the undoped GaN layer  53  located under both ends of the mask layers  54  are scooped. Thus, both ends of the mask layers  54  overhang to protrude above ends of the recess portions  53   a  of the undoped GaN layer  53 . 
   Then, the mask layers  54  are employed as selective growth masks for epitaxially laterally overgrowing an undoped GaN layer  55  on the recess portions  53   a  of the undoped GaN layer  53  serving as an underlayer and the mask layers  54 , as shown in  FIG. 21 . In this case, the undoped GaN layer  55  grown on portions located under the overhangs of the mask layers  54  applies upward force to the overhangs of the mask layers  54 , whereby the upper surfaces of the overhanging mask layers  54  are curved to form dents  54   a . The undoped GaN layer  55  is further grown on the dents  54   a  to have a flat upper surface while forming voids  56  on the dents  54   a.    
   The voids  56  relax strain of the laterally grown undoped GaN layer  55 , whereby inclination of the c-axis of the undoped GaN layer  55  can be suppressed. According to the fifth embodiment, the mask layers  54  are curved to form the dents  54   a  similarly to the aforementioned third and fourth embodiments, whereby the contact areas between the upper surfaces of the mask layers  54  and the grown undoped GaN layer  55  are more reduced as compared with those in the aforementioned first and second embodiments and hence inclination of the c-axis can be reduced substantially to 0°. Thus, according to the fifth embodiment, the undoped GaN layer  55  can be formed with superior crystallinity to those in the first and second embodiments. 
   According to the fifth embodiment, raw material is hardly supplied to portions located under the overhangs of the mask layers  54  in growth of the undoped GaN layer  55 , to cause difference in growth rate between the portions located under the overhangs and the remaining portions. Thus, lateral growth is dominant from an extremely initial stage in the portions located under the overhangs having a low growth rate, whereby dislocations  57  start to laterally bend from the initial stage, as shown in  FIG. 22 . Therefore, the dislocations  57  hardly reach the upper surface of the undoped GaN layer  55 . Thus, the number of dislocations  57  of the undoped GaN layer  55  can be more reduced as compared with the prior art shown in  FIG. 31 . Consequently, inclination of the c-axis of the undoped GaN layer  55  can be reduced substantially to 0° while reducing the number of dislocations  57  in the fifth embodiment. Thus, the undoped GaN layer  55  can be formed with superior crystallinity to those in the aforementioned first to fourth embodiments. 
     FIG. 23  is a sectional view showing a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the fifth embodiment. Referring to  FIG. 23 , layers  11  to  16 , electrodes  17  and  18  and protective films  19  similar to those of the first embodiment shown in  FIG. 5  are formed on the undoped GaN layer  55  shown in  FIG. 22  in the semiconductor laser device according to the fifth embodiment. The layers  11  to  16  are formed on the undoped GaN layer  55  having substantially no inclination of the c-axis and a further reduced number of dislocations formed by the method shown in  FIGS. 20 to 22  in the semiconductor laser device according to the fifth embodiment, whereby superior crystallinity can be implemented in the layers  11  to  16 . Consequently, a semiconductor laser device having superior device characteristics can be obtained according to the fifth embodiment. 
   (Sixth Embodiment) 
   Referring to  FIGS. 24 to 27 , a sixth embodiment of the present invention is described with reference to a case of directly growing a nitride-based semiconductor layer on a substrate without employing an underlayer in the aforementioned fifth embodiment. A method of forming a nitride-based semiconductor according to the sixth embodiment is now described with reference to  FIGS. 24 to 27 . 
   First, mask layers  62  of SiO 2  or SiN are formed on prescribed regions of an n-type Si substrate  61  to have a thickness of about 0.2 μm and a width of about 4 μm, as shown in  FIG. 24 . In this case, the mask layers  62  are formed in the shape of stripes in a cycle of about 7 μm. The mask layers  62  are employed as masks for wet-etching the n-type Si substrate  61 , thereby forming recess portions  61   a  on the n-type Si substrate  61 . The recess portions  61   a  are formed by etching the n-type Si substrate  61  until portions located under both ends of the mask layers  62  are scooped. Thus, both end portions of the mask layers  62  overhang to protrude above ends of the recess portions  61   a  of the n-type Si substrate  61 . 
   Then, the overhanging mask layers  62  are employed as masks for growing low-temperature buffer layers  63  of GaN or AlGaN on the surfaces of the recess portions  61   a  of the n-type Si substrate  61  by MOCVD or HVPE in a thickness of about 20 nm to about 30 nm, as shown in  FIG. 25 . 
   Then, the overhanging mask layers  62  are employed as selective growth masks for epitaxially laterally overgrowing an undoped GaN layer  64  by MOCVD or HVPE on the low-temperature buffer layers  63  and the mask layers  62 , as shown in  FIG. 26 . In this case, the undoped GaN layer  64  grown on portions located under the overhangs of the mask layers  62  applies upward force to the overhangs of the mask layers  62 , whereby the upper surfaces of the mask layers  62  are curved to form dents  62   a . The undoped GaN layer  64  is further grown on the dents  62   a , to have a flat upper surface while forming voids  65  on the dents  62   a.    
   The voids  65  formed by curving the mask layers  62  reduce the contact areas between the upper surfaces of the mask layers  62  and the undoped GaN layer  64 , whereby inclination of the c-axis of the laterally grown undoped GaN layer  64  can be reduced substantially to 0°, similarly to the aforementioned fifth embodiment. 
   According to the sixth embodiment, raw material is hardly supplied to portions located under the overhangs of the mask layers  62  in growth of the undoped GaN layer  64 , to cause difference in the growth rate of the undoped GaN layer  64  between the portions located under the overhangs and the remaining portions. Thus, lateral growth is dominant from an extremely initial stage in the portions located under the overhangs having a low growth rate, whereby dislocations  66  start to laterally bend from the initial stage, as shown in  FIG. 27 . Therefore, the dislocations  66  can be more effectively prevented from reaching the surface of the undoped GaN layer  64 . Thus, according to the sixth embodiment, the number of dislocations  66  of the undoped GaN layer  64  can be more reduced as compared with the prior art shown in  FIG. 31 . Consequently, inclination of the c-axis can be reduced substantially to 0° while reducing the number of dislocations  66  in the sixth embodiment, whereby the undoped GaN layer  64  having superior crystallinity can be obtained similarly to the fifth embodiment. 
   In the sixth embodiment, further, the undoped GaN layer  64  is directly formed o the n-type Si substrate  61  through the low-temperature buffer layers  63  without employing a GaN underlayer dissimilarly to the aforementioned fifth embodiment, whereby the fabrication process can be more simplified as compared with the fifth embodiment due to absence of the GaN underlayer. 
     FIG. 28  is a sectional view showing a semiconductor laser device fabricated with the aforementioned method of forming a nitride-based semiconductor according to the sixth embodiment. Referring to  FIG. 28 , the conductive n-type Si substrate  61  is employed in the sixth embodiment dissimilarly to the semiconductor laser devices according to the aforementioned first to fifth embodiments, and hence an n-side electrode  78  is provided on the back surface of the n-type Si substrate  61 . 
   An n-type GaN contact layer  71  doped with Si is formed on the undoped GaN layer  64  shown in  FIG. 26  in a thickness of about 5 μm. An n-type In 0.1 Ga 0.9 N anti-cracking layer  72  doped with Si is formed on the n-type GaN contact layer  71  in a thickness of about 0.1 μm. An n-type Al 0.08 Ga 0.92 N cladding layer  73  doped with Si is formed on the n-type In 0.1 Ga 0.9 N anti-cracking layer  72  in a thickness of about 1 μm. An MQW emission layer  74  having a quantum well structure is formed on the n-type Al 0.08 Ga 0.92 N cladding layer  73 . The compositions and the thicknesses of layers forming the MQW emission layer  74  are identical to those of the MQW emission layer  14  according to the first embodiment shown in  FIG. 5 . 
   A p-type Al 0.08 Ga 0.92 N cladding layer  75 , doped with Mg, having a thickness of about 0.4 μm is formed on the MQW emission layer  74 . A p-type GaN contact layer  76 , doped with Mg, having a thickness of about 0.1 μm is formed on the p-type Al 0.08 Ga 0.92 N cladding layer  75 . A p-side electrode  77  is formed on the p-type GaN contact layer  76 . The aforementioned layers  71  to  76  are examples of the “nitride-based semiconductor element layer” according to the present invention. 
   In the semiconductor laser device according to the aforementioned sixth embodiment, the layers  71  to  76  are formed on the undoped GaN layer  64  having a more reduced number of dislocations with inclination of the c-axis reduced substantially to 0° formed by the method shown in  FIGS. 24 to 27 , whereby superior crystallinity can be implemented in the layers  71  to  76 . Therefore, a semiconductor laser device having superior device characteristics can be obtained according to the sixth embodiment. 
   Although the present invention has been described and illustrated in detail, it is clearly understood that the same is by way of illustration and example only and is not to be taken by way of limitation, the spirit and scope of the present invention being limited only by the terms of the appended claims. 
   While the mask layers having recess portions or dents are made of SiN or SiO 2  in each of the aforementioned embodiments, for example, the present invention is not restricted to this but the mask layers may alternatively be made of another insulator film material or high melting point metal material. 
   While the overhanging mask layers are formed by etching two types of SiN layers formed by plasma CVD at different RF power levels in each of the aforementioned third and fourth embodiments, the present invention is not restricted to this but the overhanging mask layers may alternatively be formed by another method. For example, it is also possible to form overhanging mask layers by forming lower first mask material layers of SiO 2  having a thickness of about 0.05 μm by EB (Electron Beam) evaporation and upper second mask material layers of SiN having a thickness of about 0.45 μm by plasma CVD with RF power of 250 W and thereafter etching the first and second mask material layers. This is because the lower first mask material layers formed in the aforementioned manner are easier to etch as compared with the upper second mask material layers. 
   While the mask layers having recess portions are formed by different methods in the aforementioned first and second embodiments, the present invention is not restricted to this but mask layers formed by the method according to the second embodiment may be employed in the structure according to the first embodiment, or mask layers having recess portions formed by the method according to the first embodiment may be employed in the structure according to the second embodiment. 
   While the sapphire substrate or the Si substrate is employed in each of the aforementioned embodiments, the present invention is not restricted to this but an SiC substrate, a GaN substrate, a GaAs substrate, a spinel substrate, a GaP substrate, an InP substrate, a crystal substrate, a ZnO substrate or a ZrB 2  substrate may alternatively be employed.