Title of Invention: SEMICONDUCTOR DEVICE AND METHOD FOR MANUFACTURING THEREOF Abstract: The method for manufacturing a semiconductor device comprises steps of: forming a growth mask with a plurality of openings directly or indirectly upon a substrate that comprises a material differing from GaN-based semiconductor; and growing a plurality of island-like GaN-based semiconductor layers upon the substrate using the growth mask in the (0001) plane orientation in a manner such that the 1-100 direction extends in a direction parallel to the striped openings of the growth mask. Detailed Description: TECHNICAL FIELD The present invention generally relates to a semiconductor device and a method for manufacturing thereof, especially, is preferable to apply to a semiconductor device using a gallium nitride (GaN)-based semiconductor. BACKGROUND ART In case that a high value semiconductor is obtained with high quality upon a low-priced substrate made of different materials, the industrial value is extremely high. Therefore, researches and developments have been proceeded to realize it for a long time. Especially, in a gallium arsenide (GaAs)-based semiconductor thin film growth upon a silicon (Si) substrate and a GaN-based semiconductor thin film growth upon a sapphire substrate, a relatively good semiconductor thin film can be obtained using a so-called a buffer layer technique, and have already been in practical use. However, in the conventional buffer layer technique, a lot of defects and threading dislocations exist in a semiconductor thin film grown. Therefore, the applications are stayed in a limited device such as a light-emitting diode (LED), etc. The technique that brought a new break through for the present situation is the selective area growth (SAG) technique. For example, A. Usui et al. reduced the threading dislocations in the GaN layer dramatically wherein a substrate grown a GaN layer upon a sapphire substrate applying the heretofore known buffer layer technique is used as a base substrate, and upon the substrate, an insulator film made of silicon dioxide (SiO2) is disposed in striped shape as a growth mask, and upon the portion without the insulator film (window), a GaN layer is grown selectively, and thereafter the GaN layer is laterally grown upon the insulator film (A. Usui, H. Sunakawa, A. Sasaki, and A. Yamaguchi: Jpn. J. Appl. Phys., 36, L899 (1997)). The technique has already been tried in the GaAs growth upon a Si substrate in 1982 (B-Y. Ysauer et al.: Appl. Phys. Lett., 41, 347 (1982)). The method aims to block spreading of threading dislocations from a ground layer by an insulator film and to reduce the threading dislocations by the lateral growth of a GaN layer upon the insulator film dramatically. Therefore, the method is often named ELO (Epitaxial Lateral Overgrowth) to emphasize the lateral growth. Also, the GaN selective growth upon a Si substrate laminating thin AlGaN layer as an intermediate layer has already been reported by Y. Kawaguchi et al. in 1988. According to the report, ELO is basically possible, and the orientation relationship of crystal orientation of GaN and a ground Si substrate is given (Y. Kawaguchi et al., Jpn. J. Appl. Phys., 37 (1998) p. L966). Now, the growth mask used to grow a GaN-based semiconductor by an ELO method is generally comprised with a striped mask portion with 3 to 10 μm in width and a striped window with the same width of the mask portion. In this case, the GaN layer laterally grown upon the growth mask from the window bumps into the GaN layer laterally grown from the next window and coalesces, covering the growth mask, thereby forming a joined GaN layer. In the GaN layer obtained by the above method, threading dislocations grow from the bottom surface in the window region and many dislocations by lattice mismatch exist in the joined portion. These portions can not be used as an active region of devices and have no other choice to form a striped active region in the limited region upon the stripes. The method has been tried to apply to manufacture of a narrow striped semiconductor laser, however is not put to practical use. Generally, a base substrate and a semiconductor layer differ in materials, thermal expansion coefficient is different each other, and when the substrate temperature returns to room temperature after the growth of a semiconductor layer, compressive or tensile stress generates in the upper semiconductor layer, and the whole substrate is curved widely. For example, when a GaN layer is grown upon a sapphire substrate by an ELO method, the substrate is convex to the above. On the contrary, when a GaN layer is grown upon a Si substrate or a silicon carbide (SiC) substrate, etc. by an ELO method, the substrate is convex to the below. The curvature of the substrate becomes prominent when the thickness of the semiconductor layer becomes large, and in tremendous cases, cracks (trace of crack) occur in the semiconductor layer. Also, the curvature of the substrate makes the lithography process to form a device remarkably difficult, if not causes cracks in the semiconductor layer. Also, the portion of the GaN layer on the insulator film with less threading dislocations is limited to a narrow area with about several μm by the conventional technique, so only a several μm width stripe device such as a semiconductor laser, etc. can be manufactured. The present invention aims to solve the above subjects existing in the conventional technique at a burst. That is, the subject to be solved by the present invention is to provide a semiconductor device and a method for manufacturing thereof that enable to grow an island-like GaN-based semiconductor layer made of high quality semiconductor crystal upon a substrate made of different materials suppressing the curvature of the substrate, to suppress an occurrence of cracks, etc. even if a GaN-based semiconductor layer is quite thick, and to realize easily a semiconductor device with a large area. DISCLOSURE OF INVENTION To solve the subjects, according to the present invention, there is provided a semiconductor device comprising: a substrate that comprises a material differing from GaN-based semiconductor; a growth mask with one or a plurality of striped openings disposed directly or indirectly upon the substrate; and one or a plurality of island-like GaN-based semiconductor layers grown upon the substrate using the growth mask in the (0001) plane orientation, the striped openings of the growth mask extending in a direction parallel to the 1-100 direction of the GaN-based semiconductor layer. In the semiconductor device, the growth mask is disposed directly upon a substrate that comprises a material differing from a GaN-based semiconductor, that is, is disposed directly in contact, or is disposed indirectly through an intermediate layer, etc. made of a GaN-based semiconductor. An example of a substrate that comprises a material differing from a GaN-based semiconductor is a sapphire substrate or a Si substrate, etc., but is not limited to these substrates, and as long as enables to grow a GaN-based semiconductor layer in the (0001) plane orientation, any substrates can be used. In the semiconductor device, typically, the sides of the island-like GaN-based semiconductor layer is formed with the (1-10α) plane (α is an arbitrary integer), the (11-2β) plane (β is an arbitrary integer), or planes crystallographically equivalent to these, or, sides of the island-like GaN-based semiconductor layers include the (1-10α) plane (α is an arbitrary integer). The growth mask is formed by an insulator film of a SiO2 film or a SiN film, etc. As a preferable example, the growth mask comprises a plurality of striped openings which are arranged in the first direction parallel to the 11-20 direction of the GaN-based semiconductor layers and the second direction parallel to the 1-100 direction of the GaN-based semiconductor layers periodically at the first interval and the second interval respectively and extend in the second direction; and auxiliary striped openings disposed on the bisecting line of the region between a pair of the striped openings adjacent to each other in the first direction in a manner such that the auxiliary striped openings overlap with end portions opposing each other of a pair of the striped openings adjacent to each other in the second direction for the predetermined distance, respectively. As necessary, the auxiliary striped opening may not be disposed. The width of the auxiliary striped opening may be constant in the second direction, and may be changed in the second direction. The width of the striped opening is typically constant in the second direction, but may be changed in the second direction as necessary. As another preferable example, the growth mask comprises a plurality of striped openings which are arranged in the first direction parallel to the 11-20 direction of the GaN-based semiconductor layers periodically and extend in the second direction parallel to the 1-100 direction of the GaN-based semiconductor layers; and a plurality of striped openings which are arranged periodically in the first direction at the same interval as the striped openings and shifted by a half of the interval with respect to the striped openings and extends in the second direction in a manner such that the plurality of striped openings overlap with end portions of the striped openings for the predetermined distance in the second direction. The width of these striped openings is typically constant in the second direction, but as necessary, may be changed in the second direction. The GaN-based semiconductor layer comprises appropriately according to semiconductor devices, generally, comprises more than two layers including at least one layer among an n-type layer, an undoped layer and a p-type layer. The layers comprising the GaN-based semiconductor layer are, specifically, a GaN layer, an AlGaN layer, an AlGaInN layer, an InGaN layer, etc. In case the semiconductor device has a plurality of GaN-based semiconductor layers, the distance between island-like GaN-based semiconductor layers adjacent to each other is generally 30 μm or less, preferably 10 μm or less, but is not limited to these figures. In the semiconductor device, a number of electrodes according to the types of the semiconductor device are disposed at predetermined portions. The semiconductor device is, for example, a Schottky diode, a light-emitting diode, a semiconductor laser, a photodiode, a transistor, etc., but is not limited to these. Also, according to the present invention, there is provided a method for manufacturing of a semiconductor device comprising steps of: forming a growth mask with a plurality of striped openings directly or indirectly upon a substrate that comprises a material differing from GaN-based semiconductor; and growing a plurality of island-like GaN-based semiconductor layers upon the substrate using the growth mask in the (0001) plane orientation in a manner such that the 1-100 direction of the GaN-based semiconductor layers extends in a direction parallel to the striped openings of the growth mask. In the present invention of the method for manufacturing of a semiconductor device, the explanation relating to the present invention of the semiconductor device come into effect as far as not violating the character. The method for manufacturing a semiconductor device may further comprise a step of bonding the first support substrate upon the upper surface side of the GaN-based semiconductor layers after growing the GaN-based semiconductor upon the substrate, and peeling the first support substrate and the GaN-based semiconductor layers off from the substrate, in addition, may further comprise a step of forming one or a plurality of electrodes upon the exposed surface of the GaN-based semiconductor layer after peeling the first support substrate and the GaN-based semiconductor layers off from the substrate. As necessary, the method for manufacturing a semiconductor device further comprise a step of forming one or a plurality of electrodes upon the upper surface of the GaN-based semiconductor layers after growing the GaN-based semiconductor layer upon the substrate and before bonding the first support substrate upon the upper surface side of the GaN-based semiconductor layers, or further comprise a step of removing at least a portion of, or preferably almost all, or the most preferably all of the growth mask, or further comprises both of the steps. Also, as necessary, a conductor thin film or a conductor line is formed upon the major surface of the first support substrate on the side bonded with the GaN-based semiconductor layer. The method for manufacturing a semiconductor device, as necessary, further may comprise a step of bonding the second support substrate upon the exposed surface side of the GaN-based semiconductor layer after peeling the first support substrate and the GaN-based semiconductor layers off from the substrate. The first support substrate and the second support substrate are made of elemental semiconductor, compound semiconductor, metal, alloy, nitride-based ceramics, oxide-based ceramics, diamond, carbon, plastic, etc., and may be a single layer structure, or a multilayer structure made of these materials. For the bonding of the first support substrate and the second support substrate, a metal for bonding such as solder, etc. or organic adhesive, etc. can be used, and is selected as necessary. According to the present invention, the crystallinity of the island-like GaN-based semiconductor layer laterally growing upon the growth mask from a striped opening of the growth mask is very high, and the GaN-based semiconductor layer made of high quality semiconductor crystal can be obtained. Also, when a plurality of island-like GaN-based semiconductor layers are grown, these layers are separated each other, that is, is formed in isolation, so tensile stress or compressive stress generated in each GaN-based semiconductor layer is limited within the GaN-based semiconductor layer, and the effect by these tensile stress or compressive stress does not fall upon the other GaN-based semiconductor layers. Also, as the growth mask and the GaN-based semiconductor layer are not bonded chemically, the stress in the GaN-based semiconductor layer can be relaxed by the slide causing at the interface between the growth mask and the GaN-based semiconductor layer. Also, by existence of gaps between the island-like GaN-based semiconductor layers each other, the whole substrate growing a plurality of island-like GaN-based semiconductor layers has the flexibility, therefore, it is easily deformed when external force is applied, and can be bended. Therefore, even if there occurs slightly warpage, curvature, deformation in the substrate, they can be easily corrected by small external force, handling of substrates by vacuum chucking is possible, the manufacturing process of semiconductor devices can be easily carried out. As explained, island-like GaN-based semiconductor layers made of high quality semiconductor crystal can be grown suppressing the curvature of the substrate, and further even the GaN-based semiconductor layer is very thick, the occurrence of crack, etc. can be suppressed, thereby a large area semiconductor device can be easily realized. BRIEF DESCRIPTION OF DRAWINGS FIG. 1A and FIG. 1B are cross-sectional views for explaining the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 2 is a plan view showing an example of a growth mask used in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 3 is a plan view showing another example of a growth mask used in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 4 is a schematic view for explaining the second method to prevent the coalescence of GaN-based semiconductor layers each other in the method for manufacturing the GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 5 is a schematic view for explaining the third method to prevent the coalescence of GaN-based semiconductor layers each other in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 6 is a schematic view for explaining the third method to prevent the coalescence of GaN-based semiconductor layers each other in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 7 is a schematic view for explaining the fourth method to prevent the coalescence of GaN-based semiconductor layers each other in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 8 is a drawing substitute photograph showing a scanning electron microscope image of the surface of the GaN-based semiconductor layer grown using the growth mask shown in FIG. 2 in the method for manufacturing a GaN-based semiconductor device according to the first embodiment of the present invention. FIG. 9 is a drawing substitute photograph showing a scanning electron microscope image of the surface of the GaN-based semiconductor layer grown using a growth mask which is not formed an auxiliary striped window. FIG. 10 is a plan view showing the growth mask formed for measuring the change of the amount of lateral growth according to the angle from the 11-20 direction in the longitudinal direction of a striped window in the GaN (0001) plane growth. FIG. 11 is a schematic view showing the measuring results of the change of the amount of lateral growth according to the angle from the 11-20 direction in the longitudinal direction of a striped window in the GaN (0001) plane growth. FIG. 12A and FIG. 12B are cross-sectional views for explaining the method for manufacturing a GaN-based Schottky diode according to the second embodiment of the present invention. FIG. 13A and FIG. 13B are cross-sectional views for explaining the method for manufacturing a GaN-based Schottky diode according to the second embodiment of the present invention. FIG. 14 is a plan view for explaining the method for manufacturing a GaN-based Schottky diode according to the second embodiment of the present invention. FIG. 15A and FIG. 15B are cross-sectional views for explaining the method for manufacturing a GaN-based Schottky diode according to the third embodiment of the present invention. FIG. 16A and FIG. 16B are cross-sectional views for explaining the method for manufacturing a GaN-based Schottky diode according to the fourth embodiment of the present invention. FIG. 17A and FIG. 17B are cross-sectional views for explaining the method for manufacturing a GaN-based MISFET according to the fifth embodiment of the present invention. FIG. 18A and FIG. 18B are cross-sectional views for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 19 is a cross-sectional view for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 20 is a cross-sectional view for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 21 is a cross-sectional view for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 22 is a cross-sectional view for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 23 is a perspective view for explaining the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 24 is a drawing substitute photograph showing a scanning electron microscope image of the surface of the GaN-based semiconductor layer peeled off from the base substrate in the method for manufacturing a GaN-based semiconductor device according to the seventh embodiment of the present invention. FIG. 25A and FIG. 25B are drawing substitute photographs showing a scanning electron microscope image enlarged the end portion and the central portion of the GaN-based semiconductor layer shown in FIG. 24. FIG. 26 is a cross-sectional view for explaining the method for manufacturing a GaN-based Schottky diode according to the eighth embodiment of the present invention. FIG. 27 is a plan view for explaining the method for manufacturing a large area power GaN-based Schottky diode according to the ninth embodiment of the present invention. FIG. 28 is a cross-sectional view for explaining the method for manufacturing a GaN-based light-emitting diode according to the eleventh embodiment of the present invention. FIG. 29 is a cross-sectional view for explaining the method for manufacturing a two-terminal and a three-terminal GaN-based compound semiconductor device according to the twelfth embodiment of the present invention. FIG. 30 is a schematic view showing an equivalent circuit of a two-terminal and a three-terminal GaN-based compound semiconductor device shown in FIG. 29. FIG. 31A and FIG. 31B are plan views showing an example of a growth mask used in the method for manufacturing a GaN-based semiconductor device according to the thirteenth embodiment of the present invention. FIG. 32A and FIG. 32B are plan views showing an example of a growth mask used in the method for manufacturing a GaN-based semiconductor device according to the fourteenth embodiment of the present invention. BEST MODE FOR CARRYING OUT THE INVENTION The best mode for the embodiments of the present invention (hereafter refer to embodiment) is explained in detail below. The First Embodiment A GaN-based semiconductor device and a method for manufacturing thereof according to the first embodiment are explained. In the first embodiment, as shown in FIG. 1A, first, upon a base substrate 11, a growth mask which has a plurality of striped openings (hereafter refer to a striped window) 12a and, as necessary, in addition to them a plurality of auxiliary striped openings (hereafter refer to an auxiliary striped window) to be described later is formed. As the base substrate 11, a substrate made of different materials from the GaN-based semiconductor, for example, a C-plane sapphire substrate or a (111) plane-oriented Si substrate, etc., for example upon which a GaN-based semiconductor layer such as a GaN layer, etc. is grown in the (0001) plane orientation may be used, or a C-plane sapphire substrate itself may be used. The thickness of the GaN-based semiconductor layer such as a GaN layer, etc. to be grown upon the C-plane sapphire substrate or the (111) plane-oriented Si substrate, etc. is 1 to 2 μm, for example, but is not limited to these. The growth mask 12 can be formed by forming an insulator film, for example, a SiO2 film upon the base substrate 11, for example, by a plasma chemical vapor deposition (CVD) method, etc., for example, and patterning the SiO2 film by photolithography using a predetermined photo mask and etching. The thickness of the SiO2 film is to be 0.3 μm, for example, but is not limited to the figure. The shape and configuration of the striped window 12a and the auxiliary striped window of the growth mask 12 will be described later. Next, as shown in FIG. 1B, using the growth mask 12, a GaN-based semiconductor layer 13 is grown in an island-like shape in the (0001) plane orientation by a vapor-phase deposition method, for example, a metalorganic chemical vapor deposition (MOCVD) method. In this case, first upon the surface of the base substrate 11 exposed upon the striped window 12a, a GaN-based semiconductor is selectively grown, and is continuously laterally grown upon the grown mask 12, thereby the GaN-based semiconductor layer 13 is grown upon the growth mask 12. At the growth, before an island-like GaN-based semiconductor layer 13 strikes with an adjacent island-like GaN-based semiconductor layer 13, the growth is stopped. Whether the island-like GaN-based semiconductor layer 13 is made grow from how many striped windows 12a can be decided as necessary. In FIG. 1B, a case is illustrated that one island-like GaN-based semiconductor layer 13 is grown from the striped window 12a, but one island-like GaN-based semiconductor layer 13 may be grown from two or more striped windows 12a. The GaN-based semiconductor layer 13 is composed of two or more layers including at least one layer among an n-type layer, an undoped layer, and a p-type layer, according to a GaN-based semiconductor device to be manufactured. Next, each GaN-based semiconductor layer 13 of island-like shape grown upon the growth mask 12 by the above is processed as necessary, and further, is formed with necessary electrodes (not illustrated). After this, the base substrate 11 formed a device structure as described above, for example, is chipped in a manner such that one island-like GaN-based semiconductor layer 13 is included in one chip, thereby an intended GaN-based semiconductor device is manufactured. The details of the growth mask 12 are explained. The two examples of the growth mask 12 are shown in FIG. 2 and FIG. 3. The growth mask shown in FIG. 2 comprises a plurality of striped window 12a which are arranged in the first direction parallel to the 11-20 direction of the (0001) plane-oriented GaN-based semiconductor layers 13 and the second direction parallel to the 1-100 direction of the GaN-based semiconductor layers 13 periodically at the intervals p1 and p2 respectively and extend in the second direction. The growth mask 12 has further comprises auxiliary striped windows 12b disposed on the bisecting line of the region between a pair of the striped window 12a adjacent to each other in the first direction in a manner such that the auxiliary striped windows 12b overlap with end portions opposing each other of a pair of the striped openings 12a adjacent to each other in the second direction for the length q, respectively. The auxiliary striped window 12b is, as described later, the one to prevent embossment of both end portions in the 1-100 direction of the GaN-based semiconductor layer 13. The length of the striped window 12a is a, the width is b, the length of the auxiliary striped window 12b is c, and the width is d. A portion other than the striped window 12a and the auxiliary striped window 12b in the growth mask 12 is a mask portion 12c. The length a of the striped window 12a is, for example, 200 to 2000 μm, the width b is, for example, 2 to 20 μm, the interval p1 of the striped window 12a is, for example, 6 to 120 μm, the interval p2 is, for example, 505 to 1050 μm, the length c of the auxiliary striped window 12b is given about ((p2−a)+(p1−b−d)÷tan 30°), but in case a=800 μm, b=5 μm, d=5 μm, p1=55 μm, p2=810 μm, the length c is 80 to 90 μm. The width d is, for example, the same as the width b. The width of the mask portion 12c is, for example, 50 μm as p1−b, the overlapping length q of the auxiliary striped window 12b with the striped window 12a is 35 to 40 μm in case of the above setting as (p1−b−d)÷tan 30°÷2. The growth mask 12 shown in FIG. 3 comprises a plurality of striped window 12a which are arranged in the first direction parallel to the 11-20 direction of the (0001) plane-oriented GaN-based semiconductor layers 13 periodically with the interval p1 and extend in the second direction parallel to the 1-100 direction of the GaN-based semiconductor layers 13. To prevent embossment of both end portions in the 1-100 direction of the GaN-based semiconductor layer 13 as described later, the growth mask 12 comprises further a plurality of striped windows 12a which are arranged periodically in the first direction at the same interval p1 as the striped window 12a and shifted by a half of the interval p1 with respect to the striped window 12a and extends in the second direction in a manner such that the plurality of striped windows 12a overlap with end portions of the striped windows 12a for the length r in the second direction. The length a of the striped window 12a is, for example, 200 to 2000 μm, the width b is, for example, 2 to 20 μm, the interval p1 of the striped window 12a is, for example, 6 to 120 μm, the width of the mask portion 12c is, for example, p1−b, so, in case of p1=55 μm and b=5 μm, is 50 μm. The overlapping length r of the end portions each other of the striped window 12a is (p1−b−d)÷tan 30°÷2, therefore, in case of p1=55 μm, and b=5 μm, d=5 μm, is 35 to 40 μm. Growing the GaN-based semiconductor layer 13 using the growth mask 12 shown in FIG. 2 or FIG. 3, following advantages can be obtained. Although the details are described later, in the (0001) plane growth of a GaN-based semiconductor, the lateral growth rate parallel to the plane is the biggest in the 11-20 direction, and is the smallest in the 1-100 direction. In the growth mask 12 shown in FIG. 2 or FIG. 3, as the longitudinal direction of the striped window 12a is the 1-100 direction, the growth rate of the GaN-based semiconductor is small at the both ends of the striped window 12a, the island-like GaN-based semiconductor layers 13 opposing each other in the 1-100 direction do not coalesce, and the island-like GaN-based semiconductor layers 13 can be separated each other. At this time, the size of the island-like GaN-based semiconductor layer 13 in the 1-100 direction becomes nearly equal with the length a of the striped window 12a. On the other hand, as the lateral growth rate in the 11-20 direction from the striped window 12a is very fast, it is necessary for the island-like GaN-based semiconductor layers 13 not to coalesce each other in the 11-20 direction. For this, in the first method, the distance between the striped window 12a and the striped window 12a in the 11-20 direction, that is, the width of (p1−b) of the mask portion 12c in the 11-20 direction makes larger than the designed width in the 11-20 direction of the GaN-based semiconductor layer 13. By the method, the side in the direction that intersects at right angle in the 11-20 direction of the GaN-based semiconductor layer 13 becomes a (11-20) plane or an inclined (11-2β) plane (β is an arbitrary integer). By the second method, as shown in FIG. 4, upon the growth mask 12 at the portion directly inside the end portions of the designed GaN-based semiconductor layer 13 in the 11-20 direction, a zigzag striped window 12a with a side in the equivalent directions with the 1-100 direction in which the growth rate is the smallest. By this, the lateral growth rate in the 11-20 direction of the GaN-based semiconductor layer 13 can be reduced drastically, and the coalescence of the island-like GaN-based semiconductor layers 13 each other in the 11-20 direction can be prevented. By the method, the sides of the both end portions in the 11-20 direction of the GaN-based semiconductor layer 13 become a zigzag (1-100) plane or an inclined (1-10α) plane (α is an arbitrary integer). According to the third method, as shown in FIG. 5, upon the growth mask 12 at the portion directly inside the both end portions of the designed GaN-based semiconductor layer 13 in the 11-20 direction, the striped window 12a is formed so as to have an uneven side with a linear portion parallel to the 1-100 direction in which the growth rate is the smallest, and a linear portion parallel to the 11-20 direction alternately at both sides of the mask portion 12c. In this case, growing the GaN-based semiconductor layer 13, as shown FIG. 6, at the linear portion parallel to the 1-100 direction of the side of both sides of the mask portion 12c of the striped window 12a, the GaN-based semiconductor layer 13 grows in the 11-20 direction, but at the corner crossing the linear portion parallel to the 1-100 direction and the linear portion parallel to the 11-20 direction, the growth in the 11-20 direction can not be made, and at the corner, as the result the (1-10α) plane (α is an arbitrary integer) with slow growth appear dominantly, the sides of the both ends in the 11-20 direction of the GaN-based semiconductor layer 13 become a zigzag (1-100) plane. In FIG. 5, the unevenness of a pair of sides opposing each other of the striped window 12a at both sides of the mask portion 12c is shifted by a half of the interval in the 1-100 direction each other, but the shifted amount is not limited especially, for example, may be shifted by an interval in the 1-100 direction. According to the third method, as shown in FIG. 7, in the growth mask 12, along the striped window 12a extending in the 1-100 direction, a dot-like opening (hereafter refer to a dot window) 12d of a square or a rectangle made of a side parallel to the 1-100 direction and a side parallel to the 11-20 direction is formed in the 1-100 direction in a plural number, preferably with equal distance, and is separated from each other. In this case, growing the GaN-based semiconductor layer 13, the growth of the GaN-based semiconductor layer 13 is blocked at the position of the dot window 12d, and the result is that the (1-10α) plane (α is an arbitrary integer) of which growth is slow appears dominantly. By the way, in the island-like GaN-based semiconductor layer 13 enclosed with planes including planes with small growth rate, when the distance between the GaN-based semiconductor layer 13 and the GaN-based semiconductor layer 13 opposing planes with small growth rate each other is large, the following disadvantages occur. That is, in the mask portion 12c of the growth mask 12 of the region between the GaN-based semiconductor layer 13 and the GaN-based semiconductor layer 13, as the raw gas is not consumed there, the gas concentration goes up, and the concentration gradient is generated in the direction joining the GaN-based semiconductor layer 13 and the GaN-based semiconductor layer 13, and by the diffusion according to the concentration gradient, a lot of raw gas is supplied at the edge portion of the GaN-based semiconductor layer 13. As the result, the thickness of the edge portion of the GaN-based semiconductor layer 13 becomes larger in comparison with other portions, and becomes a raised shape. More specifically, at the mask portion 12c of the growth mask 12 of the region between the GaN-based semiconductor layer 13 and the GaN-based semiconductor layer 13 in the 1-100 direction of which growth rate is the smallest, the raw gas is not consumed there, therefore the gas concentration goes up, and the concentration gradient in the 1-100 direction is generated, and by the diffusion according to the concentration gradient, a lot of raw gas is supplied at the edge portion in the 1-100 direction of the GaN-based semiconductor layer 13. As the result, the thickness of the edge portion in the 1-100 direction of the GaN-based semiconductor layer 13 becomes larger in comparison with other portions, and becomes a raised shape. The specific raised shape of the edge portion of the GaN-based semiconductor layer 13 causes not only structural inconveniences of a GaN-based semiconductor device but also creates problems in the following manufacturing processes of photolithography, etc. To prevent ununiformity of the thickness of the island-like GaN-based semiconductor layer 13 caused by a specific raised shape of the edge portion, the GaN-based semiconductor layer 13 and the GaN-based semiconductor layer 13 come close as much as possible, and it is necessary not to create in-plane ununiformity of raw gas from the beginning of the growth. For this, in the growth mask 12 shown in FIG. 2, upon the bisecting line of the region between a pair of striped windows 12a adjacent to each other in the 11-20 direction, the auxiliary striped window 12b is formed in a manner such that the auxiliary striped window 12b overlap with the opposing end portions of the striped windows 12a adjacent to each other in the 1-100 direction for the length q, respectively, in other words, the auxiliary striped window 12b is formed in the center of the region coming cross the four end portions of four striped windows 12a, thereby in-plane uniformity of gas concentration can be obtained by the consumption of raw gas caused by growing the island-like GaN-based semiconductor layer 13 from the auxiliary striped windows 12b also. Also, in the growth mask 12 shown in FIG. 3, the striped window 12a is arranged shifting by a half of the interval p1 in the 11-20 direction each other, and the end portions of the striped window 12a in the 1-100 direction is overlapped for the length r each other, in other words, the striped windows 12a each other arranged by shifting by a half of the interval p1 in the 11-20 direction is penetrated by the length r in the 1-100 direction, thereby in-plane uniformity of gas concentration can be obtained. A scanning electron microscope image (SEM image) of the surface of the GaN-based semiconductor layer 13, here a GaN layer grown into an island-like shape by a MOCVD method using the growth mask 12 shown in FIG. 2 is shown in FIG. 8. Here, as the base substrate 11, a substrate grown a 2-μm-thick GaN layer upon a C-plane sapphire substrate is used. The growth mask 12 is formed with a 0.3-μm-thick SiO2 film, the length a of the striped window 12a is 800 μm, the width b is 5 μm, the interval p1 of the striped window 12a is 55 μm, the interval p2 is 810 μm, the width of the mask portion 12c is 50 μm, the length c of the auxiliary striped window 12b is 80 μm, the width d is 5 μm, the distance between the striped window 12a and the striped window 12a in the 1-100 direction is 10 μm, the overlapping length q between the end portion of the striped window 12a and the auxiliary striped window 12b is 35 μm. The length c=80 μm of the auxiliary striped window 12b is obtained by dividing the width 50 μm of the mask portion 12c with tan 30°. The thickness of the GaN layer grown into an island shape is 5 μm. The growth of the GaN layer is made at the temperature of 1100° C., and the pressure of 30 kPa. At the growth of the GaN layer, trimethylgallium (TMG) and ammonia (NH3) are used as raw gas, and hydrogen (H2) and nitrogen (N2) are used as carrier gas. As shown in FIG. 8, the GaN-based semiconductor layer 13 is grown into a long and thin hexagonal island shape centering each a striped window 12a, and the GaN-based semiconductor layer 13 is grown into a rhombic island shape centering each auxiliary striped window 12b, and the swell at the edge portion in the 1-100 direction of the thin and long hexagonal island-like GaN-based semiconductor layer 13 can be prevented. The arrow in FIG. 8 shows the 1-100 direction. On the other hand, the SEM image of the surface of the GaN-based semiconductor layer 13 grown into an island shape using a growth mask without the auxiliary striped window 12b is shown in FIG. 9. As shown in FIG. 9, the edge portion of the both ends in the 1-100 direction of the long and thin hexagonal island-like GaN-based semiconductor layer 13 has a swelling portion. In case forming one side surface of the island-lake GaN-based semiconductor layer 13 by the plane in the direction intersecting at right angle with the 1-100 direction, the side growth is stopped as described, so the distance between the GaN-based semiconductor layers 13 adjacent to each other is large, the thickness of the edge portions of the GaN-based semiconductor layer 13 in the 1-100 direction becomes large, which causes problems in the following photolithography process. Therefore, the distance between the GaN-based semiconductor layers 13 adjacent to each other is needed to become small as much as possible. According to the experiment, the distance is 20 μm or less, preferably 10 μm or less. Next, explained are details about that in the (0001) plane growth of a GaN-based semiconductor, the lateral direction growth rate in the direction parallel to the plane is the largest in the 11-20 direction, and is the smallest in the 1-100 direction. As a base substrate, a substrate grown a 2-μm-thick GaN layer upon a C-plane sapphire substrate by an MOCVD method is used. Next, upon the base substrate, a 0.3-μm-thick SiO2 film is formed by a plasma CVD method. Next, as shown in FIG. 10, the striped window 12a, 800 μm in length and 20 μm in width each, is formed in fan shapes every 10° angle by photolithography and etching. The lateral direction in FIG. 10 is angle 0°. The direction of the angle 0° is in the direction which the longitudinal direction of the striped window 12a is in the 11-20 direction, and the direction that GaN grows in just the 1-100 direction from the striped window 12a. The substrate formed the striped window 12a in a fan shape upon abase substrate is brought in an MOCVD device again, and by an MOCVD method, GaN layer is selectively grown from the striped window 12a, and the lateral growth amount (length) of GaN layer upon the growth mask 12 is measured. The growth of the GaN layer is made at the temperature of 1100° C. and the pressure of 30 kPa. At the growth of the GaN layer, TMG and NH3 are used as raw gas, and H2 and N2 are used as carrier gas. The results are shown in FIG. 11. The abscissa axis in FIG. 11 is the angle from the GaN 11-20 direction of the longitudinal direction of the striped window 12a, and the vertical axis shows the lateral growth amount upon the growth mask 12a. As shown in FIG. 11, when the angles are 30° and 90° from the 11-20 direction of the longitudinal direction of the striped window 12a, in other words, when the longitudinal direction of the striped window 12a is in the 1-100 direction, the lateral growth amount of the GaN layer upon the growth mask 12 in the 11-20 direction is about 14 μm. For this, when the angle from the 11-20 direction of the longitudinal direction of the striped window 12a is 0° and 60°, in other words, when the longitudinal direction of the striped window 12a is in the 11-20 direction, the lateral growth amount upon the growth mask 12 in the 1-100 direction is about 3 μm, which is quite small. Accordingly, it can be said that the GaN layer does not grow in the 1-100 direction practically. As well, the side of the GaN layer in the 1-100 direction tends to incline, and in the (1-10α) plane, α is between −2 to 2. The α=0 is a vertical plane. Accordingly, in case growing an island-like GaN-based semiconductor layer, it is possible to lay out with the (1-100) plane. According to the first embodiment, the crystallinity of the GaN-based semiconductor layer 13 grown upon the growth mask 12 from a plurality of striped windows 12a of the growth mask 12 is quite good. Also, as a plurality of the island-like GaN-based semiconductor layers 13 are formed by separating each other, the tensile stress or compressive stress generated in each GaN-based semiconductor layer 13 at the growth and the recovery to room temperature is limited only in the GaN-based semiconductor layer 13, and these tensile stress or compressive stress do not affect other GaN-based semiconductor layers 13. Also, the growth mask 12 and the GaN-based semiconductor layer 13 are not chemically bonded, so the stress in a GaN-based semiconductor layer 13 is relaxed by slide occurred at the interface between the growth mask 12 and the GaN-based semiconductor layer 13. Also, as gaps exist between island-like GaN-based semiconductor layers 13 each other, the base substrate 11 grown the GaN-based semiconductor layer 13 as a whole has flexibility, and when external force is applied, the base substrate 11 is easily deformed and can be bended. Therefore, even if small warpage, curvature and deformation, etc. exist in the base substrate 11, it is possible to correct them easily by small external force, and the handling of the base substrate 11 by vacuum chucking becomes possible, and the manufacturing process of a GaN-based semiconductor device can be executed easily. From the above, the island-like GaN-based semiconductor layer 13 made of high quality semiconductor crystal can be grown suppressing curvature of the base substrate 11, further even the GaN-based semiconductor layer 13 is very thick, the generation of cracks, etc. can be suppressed, thereby a large area GaN-based semiconductor device can be realized easily. The Second Embodiment A GaN-based Schottky diode and the method for manufacturing thereof according to the second embodiment are explained. First, as the same as the first embodiment, as shown in FIG. 12A, a growth mask 22 is formed upon a base substrate 21. As the base substrate 21, a substrate grown a 2-μm-thick GaN layer upon a C-plane sapphire substrate is used. The growth mask 22 comprises a striped window 22a and an auxiliary striped window (not illustrated) as the same as the growth mask 12 shown in FIG. 2, and the striped window 22a of the growth mask 22 directly inside portion of both end portions of a designed GaN-based semiconductor layer in the 11-20 direction has zigzag shape with a side in equivalent directions as the 1-100 direction as shown in FIG. 4. For example, the growth mask 22 is formed with a 0.3-μm-thick SiO2 film, the length a of the striped window 22a is 800 μm, the width b is 5 μm, the interval p1 of the striped window 22a is 55 μm, the interval p2 is 810 μm, the width of a mask portion is 50 μm, the length c of the auxiliary striped window is 80 μm, the width d is 5 μm, the distance between the striped window 22a and the striped window 22a in the 1-100 direction is 5 μm, the overlapping length q of the end portion of the striped window 22a and the auxiliary striped window 22b is 35 μm. Next, as shown in FIG. 12B, using the growth mask 22, an n+-type GaN layer 23 doped with Si as an n-type impurity is grown into an island-like shape in the (0001) plane orientation by an MOCVD method. The thickness of the n+-type GaN layer 23 is, for example, 8 μm, the impurity concentration is, for example, 5×1018 cm−3. The distance between the n+-type GaN layer 23 and the n+-type GaN layer 23 is, for example, about 10 μm. The growth of the n+-type GaN layer 23 is, for example, made at the temperature of 1100° C. and the pressure of 30 kPa. At the growth of the n+-type GaN layer 23, for example, TMG and NH3 are used as raw gas, H2 and N2 are used as carrier gas, silane (SiH4) diluted with nitrogen is used as n-type dopant. In this case, one island-like n+-type GaN layer 23 is the one grown from five striped windows 22a. Also, the two striped window 12a of both sides in the 11-20 direction among these five striped windows 22a are zigzag shape as shown in FIG. 4, and serve to stop the lateral growth in the 11-20 direction of the n+-type GaN layer 23. Next, the growth pressure is increased to 80 kPa, for example, to promote growth in the vertical direction, and an n-type GaN layer 24 is grown upon the n+-type GaN layer 23 by an MOCVD method adjusting crystal growth conditions. The thickness of the n-type GaN layer 24 is, for example, 5 μm, the impurity concentration is, for example, 1×1016 cm−3. Thus, the distance in the 11-20 direction of the whole n+ type GaN layer 23 and the n-type GaN layer 24 after growing the n-type GaN layer 24 is, for example, about 5 μm. As shown in FIG. 12B, in the n+-type GaN layer 23 and the n-type GaN layer 24, threading dislocations 25 are formed at the directly above portion of the striped window 22a, and at the portion joined with the n+-type GaN layers 23 each other laterally grown from striped windows 22a adjacent to each other. Next, as shown in FIG. 13A, for example, after forming an insulator film, for example, a 1-μm-thick SiO2 film 26, upon the whole surface by a plasma CVD method, for example, the SiO2 film 26 is patterned into a predetermined shape by photolithography and etching, the n-type GaN layer 24 is partially exposed. Next, using the SiO2 film 26 patterned into the predetermined shape in this way as a mask, the n-type GaN layer 24 is etched and removed by an inductively coupled plasma (ICP)-reactive ion etching (RIE) using chlorine-based etching gas, for example, and the n+-type GaN layer 23 is exposed. Next, as shown in FIG. 13B, for example, after forming an ohmic metal film upon the whole surface by, for example, a vacuum evaporation method, the ohmic metal film is patterned into a predetermined shape by photolithography and etching, and an ohmic electrode 27 is formed upon the exposed n+-type GaN layer 23. After this, an RTA (Rapid thermal annealing) is done at 800° C., for 30 seconds, for example, the ohmic electrode 27 is made an ohmic contact with the n+ type GaN layer 23. As the ohmic metal film, for example, a multilayer film of titanium (Ti)/aluminum (Al)/titanium (Ti)/gold (Au) in order from the bottom is used. The thickness of each film is, for example, a Ti film of the first layer is 10 nm, an Al film is 300 nm, a Ti film
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