Patent Publication Number: US-9837578-B2

Title: Light emitting device having light extraction structure and method for manufacturing the same

Description:
This application is a Continuation of co-pending application Ser. No. 14/151,613, filed on Jan. 9, 2014, which is a Divisional of application Ser. No. 13/612,343 (now U.S. Pat. No. 8,648,376), filed on Sep. 12, 2012, which is a Continuation of application Ser. No. 13/214,871 (now U.S. Pat. No. 8,283,690), filed on Aug. 22, 2011, which is a Continuation of application Ser. No. 12/637,653 (now U.S. Pat. No. 8,008,103), filed on Dec. 14, 2009, which is a Divisional of application Ser. No. 11/797,727 (now U.S. Pat. No. 7,652,295), filed on May 7, 2007, which claims the benefit of Korean Patent Application No. 10-2006-0041006, filed on May 8, 2006, Korean Patent Application No. 10-2007-0037414, filed on Apr. 17, 2007, Korean Patent Application No. 10-2007-0037415, filed on Apr. 17, 2007, and Korean Patent Application No. 10-2007-0037416, filed on Apr. 17, 2007. All of the above applications are hereby incorporated by reference as if fully set forth herein. 
    
    
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a light emitting device and a method for manufacturing the same, and more particularly, to a light emitting device capable of achieving an enhancement in emission efficiency and an enhancement in reliability and a method for manufacturing the same. 
     Discussion of the Related Art 
     Light emitting diodes (LEDs) are well known as a semiconductor light emitting device which converts current to light, to emit light. Since a red LED using GaAsP compound semiconductor was made commercially available in 1962, it has been used, together with a GaP:N-based green LED, as a light source in electronic apparatuses, for image display. 
     The wavelength of light emitted from such an LED depends on the semiconductor material used to fabricate the LED. This is because the wavelength of the emitted light depends on the band-gap of the semiconductor material representing energy difference between valence-band electrons and conduction-band electrons. 
     Gallium nitride (GaN) compound semiconductor has been highlighted in the field of high-power electronic devices including light emitting diodes (LEDs) because it exhibits a high thermal stability and a wide band-gap of 0.8 to 6.2 eV. 
     One of the reasons why GaN compound semiconductor has been highlighted is that it is possible to fabricate semiconductor layers capable of emitting green, blue, and white light, using GaN in combination with other elements, for example, indium (In), aluminum (Al), etc. 
     Thus, it is possible to adjust the wavelength of light to be emitted, in accordance with the characteristics of a specific apparatus, using GaN in combination with other appropriate elements. For example, it is possible to fabricate a blue LED useful for optical recording or a white LED capable of replacing a glow lamp. 
     By virtue of the above-mentioned advantages of the GaN-based material, techniques associated with GaN-based electro-optic devices have rapidly developed since the GaN-based LEDs became commercially available in 1994. 
     The brightness or output of an LED manufactured using the above-mentioned GaN-based material mainly depends on the structure of an active layer, the extraction efficiency associated with external extraction of light, the size of the LED chip, the kind and angle of a mold used to assemble a lamp package, the fluorescent material used, etc. 
     SUMMARY OF THE INVENTION 
     Accordingly, the present invention is directed to a light emitting device and a method for manufacturing the same that substantially obviate one or more problems due to limitations and disadvantages of the related art. 
     An object of the present invention is to provide a light emitting device having a structure capable of achieving an enhancement in extraction efficiency while maintaining desired electrical characteristics when a light extracting structure is introduced into the light emitting device, and exhibiting an optimal extraction efficiency in cooperation with a photonic crystal structure, and a method for manufacturing the light emitting device. 
     Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the structure particularly pointed out in the written description and claims hereof as well as the appended drawings. 
     To achieve these objects and other advantages and in accordance with the purpose of the invention, as embodied and broadly described herein, a light emitting device comprises: a semiconductor layer; and a light extracting layer arranged on the semiconductor layer and made of a material having a refractive index equal to or higher than a reflective index of the semiconductor layer. 
     In another aspect of the present invention, a light emitting device comprises: a photonic crystal layer including at least two photonic crystal structures arranged in the same plane on a semiconductor layer, the photonic crystal structures having different periodicities. 
     In another aspect of the present invention, a light emitting device comprises: a photonic crystal layer including a first photonic crystal having a periodic structure and a second photonic crystal having a random structure, the first and second photonic crystals being arranged in the same plane on a semiconductor layer. 
     In another aspect of the present invention, a light emitting device comprises: a reflective electrode; a semiconductor layer arranged on the reflective electrode, the semiconductor layer including a light emitting layer; and a photonic crystal formed on the semiconductor layer, wherein a distance between the reflective electrode and a center of the light emitting layer is 0.65λ/n to 0.85λ/n, where “λ” represents a wavelength of emitted light, and “n” represents a refractive index of the semiconductor layer. 
     In another aspect of the present invention, a light emitting device comprises: a reflective electrode; a semiconductor layer arranged on the reflective electrode, the semiconductor layer including a light emitting layer; and a photonic crystal formed on the semiconductor layer, wherein a distance between the reflective electrode and a center of the light emitting layer is an odd multiple of λ/4, where “λ” represents a wavelength of emitted light, and “n” represents a refractive index of the semiconductor layer. 
     In still another aspect of the present invention, a method for manufacturing a light emitting device comprises: growing aa plurality of semiconductor layers over a substrate; forming a first electrode on the semiconductor layer; removing the substrate; forming a dielectric layer over the semiconductor layer exposed in accordance with the removal of the substrate; forming a plurality of holes in the dielectric layer; etching a surface of the dielectric layer formed with the holes, to form a plurality of grooves in the semiconductor layer; removing the dielectric layer; and forming a second electrode on a surface of the semiconductor layer exposed in accordance with the removal of the dielectric layer. 
     It is to be understood that both the foregoing general description and the following detailed description of the present invention are exemplary and explanatory and are intended to provide further explanation of the invention as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principle of the invention. In the drawings: 
         FIG. 1  is a sectional view illustrating a structure for achieving an enhancement in the extraction efficiency of a light emitting device; 
         FIG. 2  is a graph depicting a variation in extraction efficiency depending on an increase in the refractive index of a hemisphere in  FIG. 1 ; 
         FIG. 3  is a sectional view illustrating an embodiment of a horizontal light emitting device having a photonic crystal structure; 
         FIG. 4  is a graph depicting an extraction efficiency depending on a photonic crystal depth in the structure of  FIG. 3 ; 
         FIG. 5  is a graph depicting an extraction efficiency depending on etching depth in the case in which the thickness of a semiconductor layer is limited; 
         FIG. 6  is a sectional view illustrating an embodiment of a vertical light emitting device having a photonic crystal structure; 
         FIG. 7  is a sectional view illustrating a vertical light emitting device structure for a computer simulation; 
         FIG. 8  is a sectional view illustrating the absorbance of a light emitting layer in the structure of  FIG. 7 ; 
         FIG. 9  is a photograph illustrating a radiation pattern exhibited in the case in which the light emitting layer is sufficiently spaced apart from a mirror; 
         FIG. 10  is a graph depicting the results obtained by measuring an extraction efficiency while varying the periodicity of a photonic crystal; 
         FIG. 11  is a graph depicting a variation in extraction efficiency depending on the size of holes forming the photonic crystal; 
         FIG. 12  is a graph depicting a variation in extraction efficiency depending on the etching depth of the photonic crystal; 
         FIG. 13  is a schematic view illustrating a principle that a photonic crystal structure extracts light associated with a full-reflection angle; 
         FIG. 14  is a sectional view illustrating a structure in which a photonic crystal is introduced into the top layer of a horizontal light emitting device; 
         FIG. 15  is a sectional view illustrating a light emitting device structure formed on a patterned substrate; 
         FIG. 16  is a sectional view illustrating a light emitting device structure in which both the photonic crystal and the patterned substrate are introduced; 
         FIG. 17  is a graph depicting a variation in extraction efficiency depending on the propagation distance of light in association with the photonic crystal and the patterned substrate; 
         FIGS. 18 to 21  are photographs illustrating radiation patterns of electric dipoles; 
         FIG. 22  is a schematic view illustrating an arrangement of dipoles with respect to the plane of a mirror; 
         FIG. 23  illustrates an extraction efficiency enhancement depending on the gap between the mirror and the light emitting layer and an associated radiation pattern, through a graph and photographs; 
         FIG. 24  is a photograph illustrating a radiation pattern in the case in which the gap between the light emitting layer and the mirror falls under a reinforced interference condition; 
         FIG. 25  is a graph depicting effects obtained in accordance with introduction of a photonic crystal in a structure having a reinforced interference condition; 
         FIG. 26  is a graph depicting a variation in extraction efficiency depending on the periodicity of the photonic crystal at a fixed etching depth; 
         FIG. 27  is a graph depicting a variation in extraction efficiency depending on etching depth under a reinforced interference condition; 
         FIGS. 28 to 30  illustrate a first embodiment of the present invention, in which: 
         FIG. 28  is a sectional view illustrating the first embodiment of the present invention; 
         FIG. 29  is a sectional view illustrating a horizontal light emitting device according to the first embodiment of the present invention; and 
         FIG. 30  is a graph depicting an extraction efficiency depending on the refractive index of a light extracting layer; 
         FIGS. 31 to 35  illustrate a second embodiment of the present invention, in which: 
         FIG. 31  is a sectional view illustrating one example of a horizontal light emitting device structure according to the second embodiment of the present invention; 
         FIG. 32  is a sectional view illustrating another example of the horizontal light emitting device structure according to the second embodiment of the present invention; 
         FIG. 33  is a graph depicting a transmittance depending on the incidence angles of a transparent conducting layer and a transparent metal layer; 
         FIG. 34  is a graph depicting an extraction efficiency depending on the thickness of the transparent conducting layer; and 
         FIG. 35  is a sectional view illustrating the light emitting device according to the second embodiment of the present invention; 
         FIG. 36  is a sectional view illustrating a third embodiment of the present invention; 
         FIGS. 37 to 47  illustrate a fourth embodiment of the present invention, in which: 
         FIG. 37  is a sectional view illustrating a light emitting device having periodicity-mixed photonic crystals; 
         FIG. 38  is a planar electro-microscopic photograph of the structure shown in  FIG. 37 ; 
         FIG. 39  is a sectional electro-microscopic photograph of the structure shown in  FIG. 37 ; 
         FIG. 40  is a plan view illustrating an example of the periodicity-mixed photonic crystals; 
         FIG. 41  is a sectional view corresponding to  FIG. 40 ; 
         FIG. 42  is a graph depicting an extraction efficiency of a structure in which periodicity-mixed photonic crystals are introduced; 
         FIGS. 43 to 46  are sectional views illustrating embodiments of the periodicity-mixed photonic crystals; and 
         FIG. 47  is a sectional view illustrating a vertical light emitting device having periodicity-mixed photonic crystals; 
         FIGS. 48 to 53  illustrate a fifth embodiment of the present invention, in which: 
         FIG. 48  is a sectional view illustrating an example of a light emitting device; 
         FIG. 49  is a sectional view illustrating another example of a light emitting device; 
         FIG. 50  is a graph depicting a variation in extraction efficiency depending on the thickness of an ohmic electrode in the structure of  FIG. 49 ; 
         FIG. 51  is a graph depicting a variation in extraction efficiency depending on the thickness of a p-type semiconductor layer in the structure of  FIG. 49 ; 
         FIG. 52  is a sectional view illustrating an example of a light emitting device package; and 
         FIG. 53  is a sectional view illustrating another example of the light emitting device package; 
         FIGS. 54 to 66  illustrate a sixth embodiment of the present invention, in which: 
         FIG. 54  is a sectional view illustrating the step of forming an LED structure on a substrate; 
         FIG. 55  is a sectional view illustrating the step of removing the substrate, and forming a dielectric layer; 
         FIG. 56  is a sectional view illustrating the step of arranging a mask for formation of a hole pattern in the dielectric layer; 
         FIG. 57  is a sectional view illustrating the step of forming a plurality of holes in the dielectric layer; 
         FIGS. 58 to 62  are plan views illustrating examples of various hole patterns; 
         FIG. 63  is a schematic view illustrating a dry etching process; 
         FIG. 64  is a sectional view illustrating the step of forming a photonic crystal in an n-type semiconductor layer; 
         FIG. 65  is scanning electron microscope (SEM) image of the photonic crystal structure; and 
         FIG. 66  is a sectional view illustrating the light emitting device structure. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. 
     The present invention may, however, be embodied in many alternate forms and should not be construed as limited to the embodiments set forth herein. Accordingly, while the present invention is susceptible to various modifications and alternative forms, specific embodiments thereof are shown by way of example in the drawings and will herein be described in detail. It should be understood, however, that there is no intent to limit the invention to the particular forms disclosed, but on the contrary, the invention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention as defined by the claims. 
     Like numbers refer to like elements throughout the description of the figures. In the drawings, the thickness of layers and regions are exaggerated for clarity. 
     It will be understood that when an element such as a layer, region or substrate is referred to as being “on” another element, it can be directly on the other element or intervening elements may also be present. It will also be understood that if part of an element, such as a surface, is referred to as “inner,” it is farther to the outside of the device than other parts of the element. 
     In addition, relative terms, such as “beneath” and “overlies”, may be used herein to describe one layer&#39;s or region&#39;s relationship to another layer or region as illustrated in the figures. 
     It will be understood that these terms are intended to encompass different orientations of the device in addition to the orientation depicted in the figures. Finally, the term “directly” means that there are no intervening elements. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, components, regions, layers and/or sections, these elements, components, regions, layers and/or sections should not be limited by these terms. 
     These teems are only used to distinguish one region, layer or section from another region, layer or section. Thus, a first region, layer or section discussed below could be termed a second region, layer or section, and similarly, a second region, layer or section may be termed a first region, layer or section without departing from the teachings of the present invention. 
     The extraction efficiency of a semiconductor light emitting device is determined by the refractive index difference between a semiconductor light emitting layer of the semiconductor light emitting device, from which light is emitted, and a medium (air or epoxy resin) through which the emitted light is finally observed. The extraction efficiency of a semiconductor medium is only several percentages because the semiconductor medium typically has a high refractive index (n&gt;2). 
     For example, in the case of a blue light emitting device made of a gallium nitride (n=2.4), the extraction efficiency for light emitted through a top layer of the light emitting device is only about 9% when it is assumed that the external medium is epoxy resin (n=1.4). Light other than the light emitted through the top layer is confined in the interior of the device due to a full reflection procedure, and then disappears as it is absorbed into an absorption layer such as a quantum well layer. 
     In order to enhance the extraction efficiency of such a semiconductor light emitting device, it is necessary to change the structure of the device such that light subjected to a full reflection procedure can be externally extracted. The simplest scheme for changing the structure of the semiconductor light emitting device is to coat a hemisphere made of a material having a high refractive index over the top layer of the device. 
     Since the incidence angle of light incident to a light incidence surface corresponds to an angle defined between the incident light and the light incidence surface, the incidence angle of light incident to the hemisphere is always 90° at any point on the hemisphere. The transmittance of light between two mediums having different refractive indexes is highest when the light incidence angle is 90°. Also, there is no angle, at which full reflection occurs, in any direction. 
     Practically, in the case of a semiconductor light emitting device, a hemisphere made of epoxy resin is coated over the device. In this case, the hemisphere contributes to protecting the surface of the device and enhancing the extraction efficiency of the device. 
     In  FIG. 1 , a method for more effectively obtaining the above-described effects is illustrated. The illustrated method is additional introduction of a hemisphere  3  having a refractive index similar to that of a semiconductor between an epoxy layer  1  and a semiconductor device  2 . In this case, as the refractive index of the additionally-introduced hemisphere  3  approximates to the refractive index of a semiconductor, the extraction efficiency of the semiconductor device  2  increases, as shown in  FIG. 2 . 
     This is because the critical angle between the semiconductor device  2  and the additionally-introduced hemisphere  3  increases. 
     As an example of a material exhibiting no absorption of light in a visible range and being transparent, TiO 2  may be proposed. For example, when it is assumed that a hemisphere made of the above-described material is applied to a red light emitting device, an enhancement in extraction efficiency corresponding to about 3 times the extraction efficiency of conventional cases can be theoretically obtained. 
     The additional introduction of a hemisphere having a high refractive index is a very simple and effective method. In order to apply this method, however, it is necessary to use a transparent material having a high refractive index and exhibiting no absorption of light in a light emission wavelength range. 
     Furthermore, there may be difficulties in association with processes for manufacturing a hemisphere having a size sufficiently covering the light emitting device and attaching the manufactured hemisphere to the light emitting device. 
     Another method for achieving an enhancement in external-extraction efficiency is to deform the side surfaces of a light emission structure into a pyramidal shape. This method utilizes the principle that light traveling laterally while being fully reflected within a light emitting device emerges from the top layer of the device after being reflected from the pyramidal surfaces. 
     However, this method has a drawback in that a desired enhancement is reduced as the size of the device increases. This is caused by absorption loss inevitably involved in the lateral travel of light. For this reason, in order to obtain an increased enhancement in a practical structure, it is important to cause light to be externally emitted after traveling along a path as short as possible. 
     To this end, research has been conducted to introduce a structure capable of alleviating the conditions of full reflection into a light emitting device. Representatively, there is a method in which the structure of a light emitting device is designed to have a resonator structure, to induce an output in a specific direction, starting from an initial stage, or a method in which hemispherical lenses having a size of several microns or more are arranged on the top layer of a light emitting device, to achieve an increase in critical angle. 
     However, the above-mentioned methods have not been practically used due to difficulties associated with manufacture processes. There is another method in which a rough surface having a size substantially corresponding to the wavelength of light is introduced into the output portion of a light emitting device, to achieve an enhancement in extraction efficiency through a light scattering procedure. 
     For the method for forming a rough surface on the top layer of a light emitting device, various chemical processes have been developed in association with materials used to manufacture light emitting devices. When light reaches a rough surface, a part of the light can pass through the rough surface even at an incidence angle corresponding to full reflection. 
     However, the light transmittance obtained by one scattering procedure is not so high. Accordingly, in order to expect a high light extraction effect, the same scattering procedure should be repeatedly carried out. For this reason, in the case of a light emitting device containing a material having a high absorbance, the extraction efficiency enhancement caused by the rough surface is small. 
     As compared to the above-mentioned method, when a photonic crystal having a spatially-periodic refractive index arrangement is introduced, it is possible to greatly enhance the extraction efficiency. Also, when an appropriate photonic crystal periodicity is selected, it is possible to adjust the directionality of the output of the light emitting device. Since view angle depends on the application of the light emitting device, it is considered that the design of the directionality meeting the application is an important task. 
     A large-area photonic crystal structure can be realized using holography lithography, ultraviolet (UV) photolithography, nano-imprinted lithography, or the like. Accordingly, this technique can be easily implemented for practical use thereof. 
     Efforts to enhance the extraction efficiency of a light emitting device through photonic crystals were made, starting from research for the adjustment of spontaneous emission rate using a photonic crystals. 
     Thereafter, the fact that photonic crystals contribute to an enhancement in the extraction efficiency of a light emitting device was theoretically proved. The contribution procedure of photonic crystals to the extraction efficiency enhancement is mainly summarized into two principles. 
     One principle is to cut off movement of light in a plane direction using a photonic band-gap effect, and thus, to extract light in a vertical direction. The other principle is to couple light with a mode having a high state density arranged outside a light cone in a dispersion curve, and thus, to externally extract the light. 
     The above-mentioned two principles can be independently applied in accordance with the periodicity of photonic crystals. However, it is possible to well define the photonic band-gap effect or the state density of the dispersion curve only when photonic crystals are formed under the condition in which there is a thin film which has a thickness corresponding to a half wavelength and a high refractive index contrast in a vertical direction. 
     Furthermore, since hole structures forming a photonic crystal extend through the light emitting layer, loss of a gain medium is inevitably generated. Additionally, it is impossible to avoid a reduction in internal quantum efficiency caused by surface nonradiative recombination. 
     It is considered that the photonic band-gap mirror effect or strong dispersion characteristics are applicable to specific cases because it is difficult to realize them in the structure of a general light emitting device. In order to solve this problem, a photonic crystal should be formed only on the surface of the light emitting device, without being formed on a positive medium of the light emitting device. 
     In this case, although it is impossible to utilize strong dispersion characteristics as in the case in which a photonic crystal is introduced into a thin film, it is possible to externally extract light associated with full reflection by coupling the light with a periodic structure in accordance with a general diffraction theory. 
     Currently, efforts to enhance the extraction efficiency without degrading the characteristics of a light emitting layer made of semiconductor by spatially separating a photonic crystal from the light emitting layer are being actively made. 
     Also, there was an effort to achieve an enhancement in extraction efficiency for a light emitting device using an InGaAs quantum well, in accordance with the same method as mentioned above. In addition, in association with an organic light emitting device, there was a report that it is possible to enhance the extraction efficiency of the organic light emitting device by 1.5 times, using a photonic crystal formed on a glass substrate. 
     There was also a method, in which a periodic photonic crystal structure is introduced into a semiconductor surface, to extract light confined due to full reflection, through a diffraction procedure, as mentioned above. For example, there was a report that it is possible to achieve an enhancement in extraction efficiency by forming a photonic crystal having a periodicity of 200 nm on a p-type GaN semiconductor surface. 
     In addition, there was a method in which a photonic crystal is formed even on the positive medium region of a GaN-based light emitting device, to achieve an increased enhancement in extraction efficiency using a photonic band-gap effect. In this method, however, there is a drawback of a reduction in extraction efficiency when input current increases. This is because, when a photonic crystal is introduced under the condition in which even the light emitting layer is etched, the current-voltage characteristics are particularly degraded, as mentioned above. 
     As apparent from the above description, the principle of an enhancement in external extraction efficiency of a light emitting device can be summarized into a method in which the structure of a light emitting device is changed to alleviate the conditions of full reflection, a method in which a rough surface is introduced into the surface of a light emitting device, a method in which a photonic crystal is formed in a thin film having a high refractive index contrast, to utilize a photonic band-gap effect, and a method in which a photonic crystal is separated from a light emitting layer, to externally extract light confined due to full reflection, through a diffraction procedure. 
     Of these methods, it is considered that the method, in which a periodic photonic crystal structure is introduced into the surface of a light emitting device, to achieve an enhancement in extraction efficiency, is best, taking into consideration the structure reality and efficiency enhancement of the light emitting device. 
       FIG. 3  illustrates a horizontal GaN-based light emitting device in which a GaN semiconductor layer  20  is grown over a substrate  10  made of sapphire having a refractive index (n=1.76) lower than GaN. Since the GaN semiconductor layer  20  has a total thickness reaching about 5 μm, it is considered to be a waveguide structure in which various higher modes are present. The GaN semiconductor layer  20  includes, as a top layer portion thereof, a p-type GaN semiconductor layer  21 . A multi-quantum well layer is arranged beneath the p-type GaN semiconductor layer  21 , as a light emitting layer  22 . 
     An n-type GaN semiconductor layer  23  is arranged beneath the light emitting layer  22 . A buffer layer  24  may be interposed between the n-type GaN semiconductor layer  23  and the substrate  10 . Also, a reflective film (not shown) may be formed on the substrate  10 , opposite to the GaN semiconductor layer  20 . 
     In order to uniformly supply current over the overall surface in the horizontal GaN-based light emitting device, a transparent electrode layer  30 , which is typically made of indium tin oxide (ITO), is deposited over the p-type GaN semiconductor layer  21 . Accordingly, the maximum etchable range for the introduction of a photonic crystal  40  into the horizontal GaN-based light emitting device corresponds to the sum of the thickness of the transparent electrode layer  30  and the thickness of the GaN semiconductor layer  21 . Generally, the transparent electrode  30  and p-type GaN semiconductor layer  21  have a thickness of 100 to 300 nm. 
     A calculation through a computer simulation (three-dimensional finite-difference time-domain (3D FDTD)) was conducted to identify the aspect of a variation in extraction efficiency depending on the etching depth of the photonic crystal. The results of the calculation through the computer simulation are depicted in  FIG. 4 . Referring to  FIG. 4 , it can be seen that there are two particular phenomena. 
     First, the extraction efficiency increases gently in proportion to the etching depth of the photonic crystal  40 , and then increases sharply, starting from a region where the GaN semiconductor layer  20  begins to be etched. Second, at a certain etching depth or more, there is a tendency that the extraction efficiency is saturated without further increasing. 
     Collectively taking into consideration the above-mentioned two phenomena, it can be understood that it may be necessary to introduce the photonic crystal  40  into a region including the GaN semiconductor layer  20  under the condition in which the photonic crystal  40  has a certain etching depth or more. 
     Since the etching depth, at which the extraction efficiency is saturated, is similar to the thickness of the general p-type GaN semiconductor layer  21 , it is possible to obtain a theoretical extraction efficiency saturation value without causing the region of the light emitting layer  22  to be etched. 
     However, in accordance with a practical experiment for checking a variation in light output depending on the etching depth of the photonic crystal  40 , it is found that, when the p-type GaN semiconductor layer  21  is etched to a specific depth or more, the light output is rather reduced. 
     The reason why the light output is reduced in spite of the fact that the light emitting layer  22 , namely, the quantum well structure, is not exposed is that an increase in resistance occurs due to a reduction in the volume of the p-type GaN semiconductor layer  21 . Such a resistance increase may be more serious in application fields requiring high-power light emitting devices. 
     That is, the structure of a currently-available light emitting device with a photonic crystal cannot utilize the etching depth, at which a maximum extraction efficiency is obtained, due to an increase in resistance, from an optical point of view. Therefore, the matter to be solved is to develop a new structure to which an etching depth, at which the extraction efficiency obtained by the photonic crystal is maximum, is applicable without causing an increase in resistance. 
     Referring to the graph depicting a variation in extraction efficiency depending on etching depth, which is induced through the above-mentioned computer simulation, a clue to a new structure can be obtained. One particular phenomenon found in the graph is that, when the etching depth of the photonic crystal  40  transits from the ITO transparent electrode layer  30  to the GaN semiconductor layer  20 , the extraction efficiency increases remarkably. 
     Basically, this is because the refractive index of ITO (n=1.8) is lower than the refractive index of the GaN semiconductor layer  20 . The introduction of the photonic crystal  40  into a region having a low refractive index cannot be a great help to an enhancement in extraction efficiency. This can be understood that the photonic crystal  40  functions to extract light subjected to a full reflection procedure. 
     The extraction efficiency depends on how much the photonic crystal recognizes the region of the photonic crystal  40 . Generally, when a full reflection phenomenon occurs, a surface evanescent wave is generated between two surfaces having different refractive indexes. The surface evanescent wave is present along the boundary surface of the two surfaces, and has characteristics of an exponential reduction in intensity in a direction perpendicular to the boundary surface. 
     For example, when only the ITO transparent electrode layer  30  is etched, the light associated with full reflection can recognize the photonic crystal  40  formed in the ITO transparent electrode layer  30  to a level corresponding to the intensity of the surface evanescent wave. Accordingly, it is impossible to expect a great enhancement in extraction efficiency. 
     Consequently, in order to extract a larger amount of light through the photonic crystal  40 , a strong interaction between the photonic crystal  40  and the light is required. From a physical point of view, spatial overlap between the full reflection mode formed in the GaN-based light emitting device and the structure of the photonic crystal  40  functions as an important factor. That is, in order to disturb the surface evanescent wave generated during the full reflection procedure, it is necessary to etch the GaN semiconductor layer  20 , for formation of the photonic crystal  40 . 
     Meanwhile, the etching of the GaN semiconductor layer may also mean that a material having a refractive index similar to or higher than that of the GaN semiconductor layer is etched. That is, when the formation of the photonic crystal  40  is carried out after a material having a refractive index similar to that of the p-type GaN semiconductor layer is deposited over the p-type GaN semiconductor layer, it is possible to expect effects similar to those of the above-described case, even though the p-type GaN semiconductor layer is not etched. 
     Also, when the newly-deposited material has a refractive index higher than that of GaN, properties superior to the above-described effects of the photonic crystal may be exhibited. This is because the effects of the photonic crystal depend on the refractive index difference between two materials basically forming the light extracting structure. 
     Accordingly, when a light extracting structure for an enhancement in extraction efficiency is introduced into a GaN-based light emitting device, it is possible to achieve an enhancement in extraction efficiency while maintaining desired electrical characteristics by forming a light extracting structure such as photonic crystal in a material additionally introduced over the top layer of the light emitting device, namely, the GaN semiconductor layer (typically, p-GaN), without etching the GaN semiconductor layer. 
     The maximum etchable range for the introduction of the photonic crystal  40  into a horizontal GaN-based light emitting device is limited by the thickness (100 to 300 nm) of the p-type GaN semiconductor layer  21  forming the top layer of the light emitting device. For this reason, there may be a limitation on extraction efficiency. 
       FIG. 6  illustrates an example of a vertical light emitting device. The illustrated vertical light emitting device has a structure in which the material of a substrate, namely, sapphire, is removed during a growth procedure of a GaN semiconductor layer  20 , in accordance with a laser absorption process, and a reflective ohmic electrode  50  is formed over a p-type GaN semiconductor layer  21 , using a multi-layer metal thin film made of Ni, Ag, etc. to function as both a mirror and an electrode. 
     The vertical GaN-based light emitting device is different from a general horizontal GaN-based light emitting device in that the flow direction of current is vertical due to the removal of an insulator, namely, sapphire, and the light output surface in the case of  FIG. 6  is reversed such that light is output from an n-type GaN semiconductor layer  23 . 
     The fact that current flows in a vertical direction in the vertical light emitting device structure means that it is quite probable that the supplied current can reach a light emitting layer  22 , namely, a quantum well layer. This means that an enhancement in internal quantum efficiency can be achieved. 
     Also, the vertical light emitting device structure has characteristics capable of easily discharging heat because sapphire, which is an insulator, is removed, and a conductor is formed over the p-type GaN semiconductor layer  21 . These characteristics may provide advantages upon designing a high-power light emitting device. 
     Practically, when the amount of the supplied current is larger than several hundred mA in the case of a general GaN-based blue light emitting device, the output is rather reduced. This may be analyzed to be caused by a degradation in the internal quantum efficiency of the quantum well due to an increase in the internal temperature of the device caused by the low heat conductivity of the sapphire substrate. 
     In addition to the physical characteristics of easy current flow and easy heat discharge, the vertical blue light emitting device structure has optical characteristics worth being taken into consideration in association with an enhancement in extraction efficiency. This will be described hereinafter. 
     First, the vertical light emitting device structure has an advantage in that, since the top layer of the vertical light emitting device structure is constituted by the n-type GaN semiconductor layer  23 , a photonic layer  60  can be introduced into the n-type GaN semiconductor layer  23  which is relatively thicker than the p-type GaN semiconductor layer  21 . Generally, the extraction efficiency enhancing effect obtained through the photonic crystal  60  is proportional to the etching depth until the enhancement efficiency is saturated. 
     Accordingly, it is possible to form a photonic crystal structure having a desired depth without a problem involved in the introduction of the photonic crystal, namely, an increase in resistance caused by the etching of the p-type GaN semiconductor layer, or any limitation associated with a surface nonradiative recombination caused by an active layer, namely, a quantum well layer. Also, since the periodicity for providing a maximum extraction efficiency varies slightly depending on the etching depth, it is possible to utilize structural conditions allowed by the given etching technique. 
     Also, in the vertical light emitting device, a quantum well layer (light emitting layer  22 ), which is a light emitting region, and a mirror (reflective ohmic electrode  50 ) are arranged at positions shorter than the wavelength of emitted light. 
     That is, as described above, in the structure of the vertical light emitting device, a reflective ohmic electrode  50  functioning as both a mirror and an electrode is formed over the p-type GaN semiconductor layer  21 . Accordingly, the thickness of the p-type GaN semiconductor layer  21  corresponds to the gap between the light emitting layer  22  and a metal mirror in the light emitting device. 
     Generally, when a mirror having a high reflectance is present at a position near the light emitting layer  22 , the light emission performance of the light emitting device may greatly vary, as compared to the case in which there is no mirror. That is, a variation in decay rate may occur in accordance with the gap between the light emitting layer  22  and the mirror. It may also be possible to adjust a radiation pattern in accordance with the gap between the light emitting layer  22  and the mirror. When these characteristics are appropriately used, it is possible to greatly enhance the extraction efficiency of the light emitting device. 
     Hereinafter, the procedure for determining structural factors of a photonic crystal applicable to a vertical GaN-based light emitting device and calculating a relative ratio of extraction efficiency enhancements obtainable by respective structural factors will be described. 
     The total efficiency of the vertical light emitting device structure corresponds to the efficiency obtained in accordance with vertical radiation because there is no radiation through side surfaces of the substrate in the vertical light emitting device structure, as compared to the horizontal structure. In  FIG. 7 , an example of a light emitting device structure to be analyzed through a computer simulation is illustrated. As shown in  FIG. 7 , the light emitting device structure includes a light-emitting semiconductor layer  80  formed with a photonic crystal  60 . An epoxy resin layer  70  having a refractive index of 1.4, which is usable as a sealant, is arranged outside the photonic crystal  60 . 
     It is impossible to completely include the size of a general light emitting device in the calculation structure due to a limited computer memory. In order to solve this problem, a method, in which perfect mirrors (not shown) are arranged at opposite ends of a light emitting device structure having a finite size (12 μm) was used. 
     Also, an absorbance k of 0.045 was given to the inside of the light emitting layer (quantum well layer  22 ) of the light emitting device  80 , as shown in  FIG. 8 . However, for the convenience of analysis, an actual metal mirror, which exhibits a certain absorbance and is arranged at a lower end of the structure, was replaced by a perfect mirror having a reflectance of 100%. 
     Since an interference effect by a mirror should always be taken in the vertical structure, the relative position of the light emitting layer  22  to the mirror in the structure is an important parameter. This is because, when the radiation pattern is changed due to an interference effect generated between the mirror and the light emitting layer  22 , the structural factors of the photonic crystal  60  to act effectively may be varied. That is, it may be considered that the angle of light, at which efficient light extraction occurs in accordance with a diffraction procedure, depends on the periodicity of the photonic crystal  60 . 
     In this case, it is intended to calculate only the effect obtained by the photonic crystal  60  under the condition in which mirror effects are excluded. In order to exclude interference effects caused by the mirror, the gap between the mirror and the light emitting layer  22  is set to be long or to correspond to a middle condition between a reinforced interference condition and an offset interference condition. 
     The radiation pattern obtained when the light emitting layer  22  is free of the interference effects of the mirror, as described above, is illustrated in  FIG. 9 . This radiation pattern may be considered to be a spherical wave, even though fine interference patterns are still exhibited at specific angles. 
     A variation in extraction efficiency depending on the periodicity of the photonic crystal  60  is illustrated in  FIG. 10 . As shown in  FIG. 10 , the periodicity “a” of the photonic crystal  60 , at which a maximum extraction efficiency can be obtained, is about 800 nm, and the relative enhancement in extraction efficiency is about 2 times. In this case, the etching depth was set to 225 nm, and the radius of holes  61  forming the photonic crystal  60  was set to 0.25a when “a” represents the periodicity of the photonic crystal  60 . 
     A variation in extraction efficiency depending on the size of the holes  61  forming the photonic crystal  60  is illustrated in  FIG. 11 . In this case, the etching depth was set to 225 nm, and a periodicity of 800 nm was selected. Referring to  FIG. 11 , it can be seen that, when the size of the holes  61  forming the photonic crystal  60  corresponds to 0.35a, a maximum extraction efficiency is obtained, and the relative enhancement increases to 2.4 times. 
     As described above, the vertical GaN-based light emitting device is advantageous in that the limitation on etching depth is small. Although the maximum etching depth in the horizontal structure is determined by the thickness of the p-type GaN semiconductor layer (actually, about half of the thickness of the p-GaN layer when an increase in resistance is taken into consideration), it is possible to use the thickness of the n-type GaN semiconductor layer (about 3 μm), which is much larger than the thickness of the p-type GaN semiconductor layer, in the vertical structure. 
     In order to utilize the above-described advantage of the vertical structure, an optimal periodicity depending on the etching depth for formation of the photonic crystal was checked while sequentially varying the etching depth. 
     As mentioned above in association with the research for the horizontal structure, there is a tendency that the extraction efficiency is saturated, at a certain etching depth or more. 
     However, there is an interesting fact that, when the etching depth increases, the extraction efficiency obtained by a photonic crystal structure having a long periodicity increases continuously. This is worthy of notice in that it is possible to use a photonic crystal structure having a long periodicity, which can be easily technically implemented, while increasing the etching depth. 
     The reason why the extraction efficiency of the photonic crystal structure having a long periodicity increases continuously as the etching depth increases may be analyzed as follows ( FIG. 13 ). 
     First, light can pass through two mediums having different refractive indexes, only when the phase-matching condition in a plane direction is satisfied. 
     Second, when light propagates from a medium having a high refractive index to a medium having a low refractive index, it is impossible to satisfy the phase-matching condition at a specific angle or more. This specific angle is called a “critical angle”. Full reflection occurs at the critical angle or more. 
     Third, the photonic crystal assists light associated with an angle causing full reflection to be externally extracted. That is, when the photonic crystal is coupled with light, the quantity of motion of the photonic crystal increases to allow the light associated with full reflection to satisfy the phase-matching condition. 
     Fourth, the quantity of motion of the photonic crystal is inversely proportional to the periodicity of the photonic crystal. That is, since the photonic crystal, which has a short periodicity, can generate a large quantity of motion, it can effectively extract light, which is included in light associated with full reflection, but propagates in a direction close to a horizontal direction far away from the critical angle. On the other hand, the photonic crystal, which has a long periodicity, is effective in extracting light propagating in a direction close to a vertical direction. 
     Fifth, in accordance with a theory of wave optics, the full reflection procedure carried out in a waveguide structure can be explained in association with modes. For example, light having an incidence angle close to a horizontal direction corresponds to a basic waveguide mode, and light having an incidence angle closer to a vertical direction corresponds to a higher waveguide mode. 
     Sixth, the GaN-based light emitting device can also be considered as a waveguide structure having a thickness of several microns or more. 
     Accordingly, it can be seen that the photonic crystal having a short periodicity is suitable to extract the basic wavelength mode, whereas the photonic crystal having a long periodicity is suitable to extract a higher wavelength mode. Thus, it is possible to determine an appropriate photonic crystal applicable to a GaN-based light emitting device, taking into consideration the above-described facts. 
     Generally, the basic wavelength mode exhibits a tendency of a saturation in extraction efficiency at a certain photonic crystal etching depth (˜λ/n) or more. On the other hand, the higher wavelength mode exhibits a tendency of a continuous increase in extraction efficiency at an increased photonic crystal etching depth. 
     Consequently, the extraction efficiency for a higher waveguide mode by the photonic crystal structure having a long periodicity increases continuously as the etching depth increases. 
     In order to obtain a maximum extraction efficiency, a task for optimizing the structural factors of the photonic crystal was conducted through a calculation using a computer simulation. As a result, it was found that the extraction efficiency has a close relation with etching depth, hole size, periodicity, etc. 
     In particular, in the case of a vertical GaN-based light emitting device, there is no limitation on etching depth because a relatively-thick n-type GaN semiconductor layer is used to form a photonic crystal. Accordingly, when a large etching depth is introduced, it is also possible to increase the possibility that the periodicity, which can be implemented using the current technique, is selectable. 
     As described above, the incidence angle of effectively-acting light varies depending on the periodicity of the photonic crystal. That is, in a photonic crystal having only one periodicity, there is an incidence angle range in which a relatively-low diffraction efficiency is exhibited. 
     However, in order to maximize the extraction efficiency, the photonic crystal should exhibit a high diffraction efficiency for angles larger than the critical angle. Accordingly, in the case of a photonic crystal structure having two or more mixed periodicities, superior extraction efficiency characteristics may be exhibited, as compared to a photonic crystal in which only one periodicity is independently present. 
     A similar principle may be applied to a horizontal GaN-based light emitting device. The method for introducing a photonic crystal into a horizontal GaN-based light emitting device to achieve an enhancement in external extraction efficiency may be mainly divided into two methods in accordance with the introduction position of the photonic crystal. 
     One method is illustrated in  FIG. 14 . This method is to etch a specific portion of a semiconductor layer  20  formed over a sapphire substrate  10 , namely, a p-type GaN semiconductor layer  21  arranged at the top of the light emitting device, as shown in  FIG. 14 . Where a transparent conductive layer  30  is formed over the p-type semiconductor layer  21 , the transparent conductive layer  30  is also etched. 
     The other method is illustrated in  FIG. 15 . This method is to grow a GaN semiconductor layer  20  over a patterned sapphire substrate (PSS)  12  previously formed with a pattern  11 , as shown in  FIG. 15 . 
     Meanwhile, a method to apply both the above-described structures may be implemented, as shown in  FIG. 16 . Graphs for comparison of extraction efficiencies respectively obtained in the above-described structures are shown in  FIG. 17 . 
     In the graphs, the horizontal axis represents the propagation distance of light in a calculation space, and the vertical axis represents the amount of externally-extracted light depending on the propagation distance of the light. 
     Referring to the graphs, it can be seen that, in the horizontal structure (reference), to which no periodic structure is applied, a saturation in extraction efficiency occurs before the propagation distance of light reaches 10 μm. Since the horizontal structure can extract only the light within the critical angle, most light exits in one transmission (reflection) procedure. 
     On the other hand, in the case, to which the structure of the photonic crystal  40  or the patterned sapphire substrate  12  with the pattern  11  is applied, a continuous increase in extraction efficiency is exhibited until the propagation distance of light reaches 100 μm. This is because light associated with full reflection is externally extracted in accordance with a diffraction procedure every time the light meets the periodic structure. 
     The extraction efficiency is finally saturated due to the absorbance of the inner material of the device. Accordingly, the basic principle applied to achieve an enhancement in external extraction efficiency in accordance with change of the structure or introduction of a periodic structure is to externally extract light within a propagation distance as short as possible such that the light is subjected to a reduced absorption loss. 
     From the above results, it can be seen that, when both the structure of the photonic crystal  40  and the patterned sapphire substrate  12  with the pattern  11  are applied, a maximum extraction efficiency is obtained. 
     The structure of the horizontal GaN-based light emitting device, in which the GaN semiconductor layer  20  is grown over the patterned sapphire substrate  12  formed with the pattern  11 , and the photonic crystal  40  is applied to the top of the GaN semiconductor layer  20 , may be technically defined as a structure in which photonic crystals having different periodicities are independently applied to different planes. 
     It is impossible to apply a photonic crystal structure having mixed periodicities to a vertical GaN-based light emitting device, different from the horizontal light emitting device. This is because the vertical GaN-based light emitting device has a substrate-removed structure. However, it is possible to apply a photonic crystal structure having different periodicities within one plane by utilizing the advantage of no limitation on etching depth. 
     Generally, it is possible to adjust the characteristics of the light emitting layer  22  when the gap between the light emitting layer  22  and a metal mirror having a high reflectance is shorter than the wavelength of light generated from the light emitting layer  22 . 
       FIGS. 18 to 22  depict which phenomenon does occur when an electric dipole, which generates light, is arranged at a position very close to a perfect mirror, through an FDTD computer simulation. The electric dipole means an electron vibrating in a specific direction in accordance with polarized light. 
     In accordance with an antenna theory, light generated from an electric dipole has a radiation pattern having peaks distributed in a direction perpendicular to a vibrating direction of an electron. That is, when an electric dipole is positioned in a single dielectric space where no highly-reflective mirror is present, light generated from the electric dipole has a radiation pattern having peaks distributed in a direction perpendicular to each polarization direction. 
     However, when a mirror having a high reflectance is arranged near the electric dipole at a distance shorter than the wavelength of light, a great variation in light emission characteristics occurs. In accordance with the gap between the electric dipole and the mirror, light concentrates around a vertical line sometimes, or propagates along the plane of the mirror sometimes. 
     Taking such phenomena into consideration, it is possible to achieve an enhancement in extraction efficiency by initially applying the condition for generating light mainly having vertical components from the quantum well layer, namely, the light emitting layer  22 . Also, although not depicted in  FIGS. 18 to 21 , it is possible to adjust a constant of nature, t (Decay rate corresponds to a reciprocal number of “t”), namely, the time taken for an excited electron to transit to a ground state. 
     As apparent from the above description, the feature that the light emission characteristics of the light emitting layer  22  can be adjusted mainly means the following two features. 
     One feature is that the output radiation pattern can be adjusted using an interference effect generated between light generated from the light emitting layer  22  and light reflected from the metal mirror. The other feature is that the decay rate can be adjusted through an interaction between a dipole in the light emitting layer  22  and an image dipole generated by the metal mirror. 
     The first feature can be explained using a traditional interference phenomenon of light. When the gap between the mirror and the light emitting layer  22  is sufficiently long to ignore an interference effect caused by the mirror, the light generated from the light emitting layer  22  can be considered as a spherical wave having a constant coefficient in all directions. 
     In the case in which the mirror is positioned near the light emitting layer  22  such that the radiation pattern is adjustable, occurrence of reinforced interference is advantageous in terms of extraction efficiency. 
     Again referring to the light emitting device as shown in  FIG. 6 , the gap between the light emitting layer  22  and the mirror (reflective electrode or reflective ohmic electrode  50 ) in the vertical light emitting device structure corresponds to the thickness of the p-type GaN semiconductor layer  21 . Accordingly, it is necessary to select an appropriate thickness of the p-type GaN semiconductor layer  21  forming a vertical radiation pattern, within a range causing a degradation in electrical characteristics. 
     The second feature associated with the adjustment of light emission characteristics has a close relation with fields of resonator quantum electrodynamics. However, this feature, namely, the principle of qualitatively adjusting a decay rate, can be easily explained, using the symmetry of the mirror. 
       FIG. 22  schematically shows the figures of vertically and horizontally-polarized electric dipoles arranged around the plane of a mirror  51 . In accordance with an electromagnetic field theory, the electric field on the plane of the mirror  51  should always be “0”. 
     Using this principle, the situation that electric dipoles are arranged around the mirror  51  can be realized through a combination of an electric dipole and an image dipole arranged at opposite sides of the mirror  51  while being spaced apart from the mirror  51  by the same distance. 
     For example, in the case of an electric dipole having polarities in a z-direction, the dipole moment thereof should have the same direction as that of an image dipole, in order to satisfy the electric field condition on the plane of the mirror  51 . Accordingly, as the gap between the electric dipole and the mirror  51  is reduced, an effect as if two electric dipoles overlap with each other is generated. As a result, an effect of increasing the decay rate by four times is generated. 
     On the other hand, when an electric dipole having polarities in a horizontal direction is applied to the electric field condition on the plane of the mirror  51 , an image dipole with a dipole moment in a direction opposite to that of the electric dipole is always induced. Accordingly, as the horizontally-polarized electric dipole approaches the plane of the mirror  51 , the decay rate approximates to “0”. 
     An arithmetic calculation was conducted, through an FDTD computer simulation, for a variation in extraction efficiency enhancement and a variation in the decay rate of the light emitting layer depending on a variation in output pattern, while adjusting the gap between the mirror and the light emitting layer, as shown in  FIG. 23 . In this case, the mirror was assumed as a perfect mirror having a reflectance of 100%, and the thickness of the light emitting layer was set to 12.5 mm. 
     First referring to the results as to extraction efficiency enhancement, it can be seen that an extraction efficiency peak and an extraction efficiency valley are exhibited at intervals of about ¼ wavelength of light. This is an evidence identifying that the radiation pattern is varied due to an interference effect of light, and thus, the extraction efficiency is adjusted. 
     After observing the radiation patterns at the peak and valley, it can be seen that, actually, strong emission of light in a vertical direction occurs at the peak, whereas, at the valley, there is no or little vertical light, and most light is emitted in a state of being inclined at a specific angle larger than the critical angle. 
     It can be seen that a maximum extraction efficiency is obtained when the gap between the light emitting layer and the mirror is about ¾(λ/n), and a large extraction efficiency is obtained when the gap corresponds to about an odd multiple of λ/4n. 
     In order to practically apply the interference effect obtained by the mirror to the vertical GaN-based light emitting device structure, it is necessary to solve the matters assumed in the computer simulation. In particular, although the light emitting layer was assumed approximately as a point light source, in the computer simulation, the quantum well layer of the practical light emitting device has a thickness of about 50 to 100 nm in accordance with the number of laminated pairs thereof. 
     However, when the thickness of the light emitting layer is larger than λ/4n, the interference effect by the mirror is reduced, and may finally disappear. Accordingly, it is necessary to provide a growth technique for reducing the thickness of the quantum well layer while maintaining a desired internal quantum efficiency. 
     Next, referring to the results as to decay rate variation, it can be seen that there are characteristics of an increase in decay rate as the gap between the mirror and the light emitting layer is reduced. That is, as the mirror approaches the light emitting layer, the circulation procedure of a gain medium is more rapidly carried out. However, it should be noted that a variation in decay rate does not always cause an increase in extraction efficiency. 
     The decay rate is only an index indicating how fast an electron and a hole coupled in the light emitting layer can be converted into photo energy. Accordingly, for the relation between the decay rate and the extraction efficiency, it is also necessary to take into consideration the decay rate caused by nonradiative recombination of a gain medium in the light emitting layer. 
     Although it is difficult to directly substitute a variation in extraction efficiency for a variation in decay rate, it is possible to analogize a qualitative relation that an increase in decay rate causes a more active radiative recombination, and thus, a reduction in the probability of nonradiative recombination, so that an enhancement in extraction efficiency will be induced. 
     Hereinafter, the effect of the photonic crystal when the gap between the mirror and the light emitting layer falls under the reinforced interference condition will be described. The reinforced interference condition is established when the gap corresponds to about ¾(λ/n). The radiation pattern generated under the reinforced interference condition is shown in  FIG. 24 . When this radiation pattern is compared with that of  FIG. 10 , it can be seen that a relatively large amount of light propagates in a vertical direction. 
     The results of a measurement for an extraction efficiency enhancement obtained when a photonic crystal is introduced under the above-described condition are shown in  FIG. 25 . 
     For a structure to which no photonic crystal is applied, the reinforced interference condition provides an extraction efficiency enhancement corresponding to about 2 times that of the spherical wave condition providing no or little mirror effect. The reason why the extraction efficiency enhancement in this case is higher than the extraction efficiency enhancement calculated in association with the calculation of the interference effect by the mirror (increased by 1.6 times) is that the absorbance was taken into consideration in this structure. 
     When graphs associated with the cases, to which a photonic crystal (periodicity=800 nm, and etching depth=225 nm) is applied, are compared, it can be seen that the structure, to which the reinforced interference condition is applied, exhibits best characteristics. 
     Of course, in the structure, to which the reinforced interference condition is applied, the relative enhancement exhibited across the photonic crystal is a maximum of about 1.2 times. This is because a large portion of the light generated in the light emitting layer is initially within the critical angle, so that the amount of light extracted through the photonic crystal is correspondingly reduced. 
     The results of a measurement for a variation in extraction efficiency depending on the periodicity of the photonic crystal under the reinforced interference condition are shown in  FIG. 26 . 
     In this case, the etching depth of the photonic crystal was fixed to 225 nm. Also, the size of holes forming the photonic crystal was 0.25a. In order to identify the dependency of the extraction efficiency on the periodicity of the photonic crystal under the reinforced interference condition and under a normal condition, two results thereof were depicted in one graph. 
     Referring to the results, it can be seen that there is no remarkable difference between the optimal periodicity of the photonic crystal under the reinforced interference condition and the optimal periodicity of the photonic crystal under the normal condition, and the optimal periodicities are in the vicinity of 800 nm. 
     Hereinafter, a variation in extraction efficiency depending on the etching depth of the photonic crystal will be described with reference to  FIG. 27 . 
     Under a normal condition in which the output pattern of the light emitting layer may be assumed as a spherical wave, the periodicity of the photonic crystal can be divided, with reference to a periodicity of about 1 μm, into a periodicity, in which the extraction efficiency is saturated at a certain etching depth, and a periodicity, in which the extraction efficiency increases continuously in proportion to an increase in etching depth. 
     This is because the photonic crystal can more effectively diffract fully-reflected light near the critical angle when the photonic crystal has a longer periodicity. When this principle is applied to the currently-discussed reinforced interference condition, it can be expected that the function of the photonic crystal having a longer periodicity becomes more important because radiation of light in a vertical direction is initially carried out under the above-described condition. 
     In order to verify this effect, the extraction efficiency according to the periodicity was calculated through a calculation using a computer simulation, while varying the etching depth, as shown in  FIG. 27 . After a comparison of this condition with the normal condition, it can be more clearly seen that the optimal periodicity, in which a maximum extraction efficiency is obtained, is shifted in a longer-periodicity direction as the etching depth increases. 
     For example, when the etching depth is 900 nm, the optimal periodicity is found at 2 μm or more. This corresponds to a structure which can be manufactured using the resolution of the current general photolithography, so that it is highly significant in terms of practical use. 
     First Embodiment 
     As shown in  FIG. 28 , a light extracting layer  120  is formed over a GaN-based semiconductor layer  110  previously formed over a substrate  100 , using a material having a refractive index similar to or higher than that of the semiconductor layer  110 . 
     The light extracting layer  120  may have a specific pattern. The specific pattern may form a photonic crystal having a periodic structure. The formation of such a photonic crystal may be achieved through an etching method or other patterning methods. 
     For the formation of the photonic crystal structure, a positive lithography for forming holes  121  or a negative lithography for forming rods is usable. 
     The photonic crystal pattern may be formed by forming the light extracting layer  120  in accordance with a deposition process, and then subjecting the light extracting layer  120  to a lithography process and an etching process. Alternatively, the photonic crystal pattern may be formed by performing a lithography on the semiconductor layer  110 , depositing the light extracting layer  120 , and then performing a lift-off process. 
     When the above-described photonic crystal structure is arranged on a surface of the light emitting device, it is possible to extract light confined due to full reflection, through a diffraction procedure, and thus, to achieve an enhancement in extraction efficiency. However, even in the case in which the light extracting layer  120  has a specific pattern as described above, it is also possible to enhance the extraction efficiency by forming a rough surface. 
     A transparent electrode material may be formed in the holes  121  of the light extracting layer  120 , which form the photonic crystal. For the transparent electrode material, a transparent conducting oxide (TCO)  130  may be used. 
     For the transparent conducting oxide  130 , indium tin oxide (ITO) may be used. Also, indium zinc oxide (IZO), aluminum zinc oxide (AZO), magnesium zinc oxide (MZO), or gallium zinc oxide (GZO) may be used. 
     When the semiconductor layer  110  is a gallium nitride layer, the light extracting layer  120  may have a refractive index of about 2.4 or more because the refractive index of gallium nitride is 2.4. The refractive index of the light extracting layer  120  may also be slightly lower than 2.4. 
     For the light extracting layer  120 , an oxide or a nitride may also be used. In particular, SiN or TiO 2  may be used. 
       FIG. 29  illustrates the structure of a horizontal light emitting device having the above-described light extracting layer  120 . The semiconductor layer  110  may include an n-type semiconductor layer  111 , an active layer  112 , and a p-type semiconductor layer  113  which are sequentially formed over the substrate  100  in this order. Also, the substrate  100  is made of sapphire having a refractive index of 1.78. If necessary, a buffer layer  114  may be interposed between the substrate  100  and the n-type semiconductor layer  111 . 
     The p-type semiconductor layer  113  arranged adjacent to the light extracting layer  120  may completely maintain the thickness obtained upon laminating the layer  113 , without being etched upon patterning the light extracting layer  120 . The thickness of the p-type semiconductor layer  113  may be 30 to 500 nm. Also, the light extracting layer  120  may have a thickness of 150 nm or more. 
     In  FIG. 29 , the pattern of the light extracting layer  120  is shown in an enlarged state. The pattern of the light extracting layer  120  is constituted by a plurality of holes  121  forming a photonic crystal in a GaN semiconductor. The radius, depth, and periodicity of the holes  121  may be optimized for the associated semiconductor layer  110 . 
     That is, when it is assumed that the periodicity of the holes  121 , namely, the spacing between adjacent holes  121 , is “a”, the radius of each hole  121  may be 0.1a to 0.45a, and the depth of each hole  121  may be 0.252λ/n to 10λ/n. Here, “λ” represents the wavelength of emitted light, and “n” represents the refractive index of the medium, at which the photonic crystal is formed, namely, the refractive index of the p-type semiconductor layer  113 . Also, the periodicity “a” may be 200 nm to 5,000 nm. 
     Meanwhile, it may be possible to form the photonic crystal structure by forming regular rods, in place of the holes  121 , as described above. 
     In order to form an n-type electrode  140  on the n-type semiconductor layer  111 , an etching process may be performed for the semiconductor layer  110  such that the n-type semiconductor layer  111  is exposed at one side thereof. A p-type electrode  150  may be formed on a region where the light extracting layer  120  is formed. 
     The thickness of the material forming the light extracting layer  120  can be freely determined. The structure, in which a material having a high refractive index is deposited to form a photonic crystal, is applicable to any types of light emitting devices emitting red, green, or other colors. 
     In order to identify the effects of the present invention, a variation in extraction efficiency depending on the refractive index of the light extracting layer  120  was measured for the structure according to the first embodiment, as shown in  FIG. 30 . 
     In the graph of  FIG. 30 , the vertical axis represents a relative enhancement in extraction efficiency in a general planar structure, in which no light extracting structure is introduced. 
     Referring to the results depicted in the graph, it can be seen that the extraction efficiency enhancement increases as the difference between the refractive index of the transparent conducting oxide  130  and the refractive index of the light extracting layer  120  increases. In  FIG. 30 , the broken line represents the extraction efficiency in the case in which the uppermost layer of the semiconductor layer (the p-type semiconductor layer in this case) is etched to form a photonic crystal. 
     When the refractive index of the light extracting layer  120  is in the vicinity of 2.6, an extraction efficiency enhancement similar to that of the case, in which the p-type GaN semiconductor layer is etched, is exhibited. When the light extracting layer  120  or photonic crystal is formed using a material having a higher refractive index, a superior extraction efficiency enhancement effect appears, as compared to the above-described photonic crystal structure formed in accordance with etching of the p-type semiconductor layer. 
     Therefore, the condition to be given to the light extracting layer  120  is that the light extracting layer  120  should have a refractive index similar to or higher than the refractive index of the semiconductor layer  20  (2.4), and should have a thickness of at least 150 nm (λ/n). If necessary, the thickness of the light extracting layer  120  may have a thickness of at least λ/4n. 
     Also, the material of the light extracting layer  120  should not cause absorption loss within the wavelength range of the light emitting layer in the light emitting device. The material of the light extracting layer  120  should also have an excellent physical bonding force. 
     For a material satisfying the above conditions, a silicon nitride (Si 3 N 4 ) having a refractive index of about 2.4 or a titanium oxide (TiO 2 ) having a refractive index of 3.0 is preferred. 
     When the light extracting layer  120  is formed over the semiconductor layer  110 , using a material having a refractive index similar to or higher than the refractive index of the semiconductor layer  110 , as described above, it is possible to maintain desired electrical characteristics of the light emitting device while introducing a photonic crystal into the light emitting device, for an enhancement in extraction efficiency. Also, the same light extraction effect can be exhibited even for a higher current. 
     Moreover, it is possible to realize a light extraction effect equal to or superior to that of the case in which a GaN semiconductor layer is etched to form a photonic crystal and to increase the etching depth upon forming the photonic crystal to a level causing a saturation of the extraction efficiency. 
     Second Embodiment 
     As shown in  FIG. 31 , a GaN-based semiconductor layer  201  is formed over a sapphire substrate  200  having a refractive index of 1.78. A transparent conducting layer  220  may be formed over the semiconductor layer  210 . The transparent conducting layer  220  can be used as an electrode. 
     For the transparent conducting layer  220 , indium tin oxide (ITO) may be used. Also, indium zinc oxide (IZO), aluminum zinc oxide (AZO), magnesium zinc oxide (MZO), or gallium zinc oxide (GZO) may be used. 
     A light extracting layer  230  is formed on the transparent conducting layer  220 , using a material having a refractive index similar to or higher than the refractive index of the semiconductor layer  210 . 
     The light extracting layer  230  may have a specific pattern. The specific pattern may form a photonic crystal having a periodic hole structure. The formation of such a photonic crystal may be achieved through an etching method or other patterning methods. 
     When the semiconductor layer  210  is a gallium nitride layer, the light extracting layer  230  may have a refractive index of about 2.4 or more because the refractive index of gallium nitride is 2.4. The refractive index of the light extracting layer  230  may also be slightly lower than 2.4. For the light extracting layer  230 , an oxide or a nitride may also be used. In particular, SiN or TiO 2  may be used. Such matters may be identical to those of the first embodiment. 
     Meanwhile, as shown in  FIG. 32 , a thin transparent metal layer  240  consisting of, for example, an Ni layer  241  and an Au layer  242 , may be used, in place of the transparent conducting layer  220 . The transparent metal layer  240  is sufficiently thin to allow light to pass therethrough. 
     Of course, the transparent metal layer  240  may be formed using an alloy containing Ni or Au. 
     Preferably, the transparent metal layer  240  has a thickness of several nanometers less than 10 nm. For example, the Ni layer  241  may have a thickness of 2 nm or less, and the Au layer  242  may have a thickness of 4 nm or less. 
     As described above, the transparent conducting layer  220  or transparent metal layer  240  may be formed over the semiconductor layer  210 . Where the transparent conducting layer  220  is formed using a metal oxide, it is preferred that the thickness of the transparent conducting layer  220  be sufficiently small. 
       FIG. 33  illustrates the transmittance depending on the incidence angle of light for the transparent conducting layer  220 , which is made of, for example, ITO, and the transparent metal layer  240 . Referring to  FIG. 33 , it can be seen that, when ITO is used, a great reduction in transmittance occurs at an incidence angle larger than about 45°. 
     Also, referring to  FIG. 34 , it can be seen that the extraction efficiency enhancement obtained by the light extracting layer  230  is gradually reduced as the thickness of the ITO layer increases. Accordingly, when the light extracting layer  230  has a refractive index lower than that of the semiconductor layer  210 , as described above, it is preferred that the thickness of the transparent conducting layer  220  be smaller than λ/2n (“λ” represents the wavelength of light, and “n” represents the refractive index of the transparent conducting layer). 
     Since the transparent conducting layer  220  can function as an electrode, it is more advantageous that the transparent conducting layer  220  has a thickness of λ/16n to λ/4n, when voltage characteristics are taken into consideration. 
     In the case of the transparent metal layer  240 , it is possible to determine the thickness of the transparent metal layer  240  because a desired transmittance can be maintained at most angles, as shown in  FIG. 33 . 
       FIG. 35  illustrates a light emitting device having the above-described structure. In the illustrated case, the semiconductor layer  210  includes an n-type semiconductor layer  211  arranged on the sapphire substrate  200 , a light emitting layer  212  arranged on the n-type semiconductor layer  211 , and a p-type semiconductor layer  213  arranged on the light emitting layer  212 . An undoped low-temperature buffer layer  214  may be interposed between the sapphire substrate  200  and the n-type semiconductor layer  211 . 
     A current diffusion layer  215  having a thickness of several nanometers may be formed over the p-type semiconductor layer  213 . The current diffusion layer  215  may be made of an undoped semiconductor layer. 
     In particular, for the current diffusion layer  215 , an In x Ga 1-x N layer or an In x Ga 1-x N/GaN superlattice layer may be used. The current diffusion layer  215  can function to enhance mobility of carriers, and thus to cause current to flow smoothly. In this regard, such a current diffusion layer is also called a current transport enhanced layer (CTEL). 
     The p-type semiconductor layer  213  may have a thickness of 30 to 500 nm. Also, the light extracting layer  230  may have a thickness of λ/4n or more. Here, “n” represents the refractive index of the material forming the light extracting layer  230 . 
     Matters not described in association with this embodiment may be identical to those of the first embodiment. 
     Third Embodiment 
       FIG. 36  illustrates an embodiment in which a light extracting layer  320  having a high refractive index is applied to the structure of a vertical light emitting device. 
     In this embodiment, the light extracting layer  320  is formed over a semiconductor layer  310 , using a material having a refractive index similar to or higher than the refractive index of the semiconductor layer  310 . The semiconductor layer  310  includes an n-type semiconductor layer  311 , a light emitting layer  312  arranged on the n-type semiconductor layer  311 , and a p-type semiconductor layer  313  arranged on the light emitting layer  312 . 
     The light extracting layer  320  may have a specific pattern. The specific pattern may form a photonic crystal having a periodic structure. The formation of such a photonic crystal may be achieved through an etching method or other patterning methods. 
     For the formation of the photonic crystal structure, a positive lithography for forming holes or a negative lithography for forming rods is usable. This matter may be identical to that of the first embodiment. 
     As shown in  FIG. 36 , the semiconductor layer  310  may be formed over an electrode consisting of a transparent electrode  330  having ohmic characteristics and a reflective electrode  340 . The transparent electrode  330  may be formed using a conducting oxide such as ITO, and the reflective electrode  340  may be formed using a metal such as Al or Ag. 
     The electrode may also consist of a single-layer reflective ohmic electrode (not shown), in place of the multi-layer structure consisting of the transparent electrode  330  and refractive electrode  340 . 
     The above-described structure may be arranged on a support layer  350  made of a metal or semiconductor layer. In this case, the support layer  350  can support the light emitting device structure in a procedure for removing a substrate, on which the semiconductor layer  310  has been grown, to obtain a vertical structure. 
     In this vertical light emitting device structure, an n-type electrode is formed on the light extracting layer  320  such that the n-type electrode is electrically connected to the n-type semiconductor layer  313 . Thus, current flows vertically during operation of the light emitting device. 
     Fourth Embodiment 
       FIG. 37  illustrates the structure of a photonic crystal layer  420  in which photonic crystals having different periodicities are mixed.  FIGS. 38 and 39  are electro-microscopic photographs of structures obtained when the photonic crystal layer  420  is experimentally implemented. 
     Referring to the electro-microscopic photographs, it can be seen that, when the surface of the n-type GaN semiconductor layer in the vertical structure is patterned in accordance with a general etching process, a fine pattern is additionally formed as the surface of the GaN semiconductor layer reacts with plasma of the gas used in the etching process. 
     The photonic crystal layer  420  formed in accordance with the above-described formation procedure has a periodicity-mixed structure including a periodic photonic crystal structure and an additional random structure having an average periodicity shorter than that of the periodic photonic crystal structure. 
     In order to arithmetically evaluate the effect of the periodicity-mixed structure of the photonic crystal layer  420 , an extraction efficiency comparison was conducted for structures of  FIGS. 40 and 41 , through a calculation using a computer simulation. 
     The periodicity-mixed structure of the photonic crystal layer  420  may be variously expressed. However, for the simplification of the expression, the periodicity-mixed structure was expressed in accordance with the following principle. 
     First, the structure of a first photonic crystal  421  having a relatively long periodicity as a first periodicity was introduced. The etching depth of the structure of the first photonic crystal  421  was set to 450 nm. 
     The structure of a second photonic crystal  422  having a relatively short periodicity as a second periodicity was introduced into a portion of the long-periodicity structure of the first photonic crystal  421  which was not etched. The etching depth of the short-periodicity structure of the second photonic crystal  422  was set to 225 nm. 
     The structure expression was experimentally conducted in a calculation space in accordance with a method in which the second photonic crystal  422  having a short periodicity is first defined, and then the first photonic crystal  421  having a long periodicity is introduced. 
     In this case, the periodicity, etching depth, and shape of each structure of the mixed photonic crystals  421  and  422  may be variously expressed. Accordingly, various periodicity-mixed structures may be conceived for the photonic crystal layer  420  in accordance with various combinations of the above-described structural factors. 
     Referring to the results of the calculation, it can be seen that the photonic crystal structure, in which different periodicities are mixed, always exhibits a superior extraction efficiency enhancement effect, as compared to other structures, as shown in  FIG. 42 . Therefore, if a method capable of reliably manufacturing an experimental periodicity-mixed photonic crystal structure can be provided, it is possible to expect an extraction efficiency improved over that of a single photonic crystal structure, irrespective of a combination of photonic crystal structures. 
     As described above, when a photonic crystal is formed by etching an n-type GaN semiconductor layer having a thickness of 3 μm upon introducing the photonic crystal into a vertical GaN-based light emitting device, it is possible to maintain desired electrical characteristics, as compared to a horizontal structure, in which a photonic crystal is formed at a p-type GaN semiconductor layer. Also, there is no substantial limitation on etching depth. 
     The extraction efficiency enhancement effect depending on the etching depth in a photonic structure having a single periodicity can be summarized as follows. That is, when the etching depth of the photonic crystal introduced into the n-type GaN semiconductor layer is 300 nm or more, and the periodicity of the introduced photonic crystal is 1 μm or more, but less than μm, the photonic structure, which satisfies the above two conditions, exhibit a tendency that that the extraction efficiency approaches a maximum extraction efficiency while increasing continuously in proportion to the etching depth. 
     As the etching depth increase, the optimal periodicity is shifted to a longer-periodicity direction. For example, the optimal photonic crystal periodicity is in the vicinity of 800 nm at an etching depth of 225 nm, but is 1,400 nm at an etching depth of 900 nm. 
     When there is no substantial limitation on etching depth, various periodicity-mixed photonic crystal structures can be proposed. The shape of the periodicity-mixed photonic crystal structure may be classified, in accordance with the manufacturing method thereof, as follows. 
     As shown in  FIG. 43 , the periodicity-mixed photonic crystal layer  420  may be formed over the semiconductor layer  410  by forming the first photonic crystal  421 , which has a relatively long periodicity, in accordance with an etching process, and then forming the second photonic crystal  422 , which has a relatively short periodicity, in accordance with an etching process. In this case, the second photonic crystal  422  has a random structure having an average periodicity shorter than the periodicity of the first photonic crystal  421 . 
     When the short-periodicity second photonic crystal  422  is formed after the formation of the long-periodicity first photonic crystal  421 , as described above, the second photonic crystal  422  is also formed in holes  421   a  forming the first photonic crystal  421 . Thus, the second crystal  422  can be present in the overall portion of the light emitting surface. 
     The periodicity of the first photonic crystal  421  corresponding to the longest periodicity of the photonic crystal layer  420  may be 800 to 5,000 nm. The depth of a pattern forming the first photonic crystal  421 , which has a periodicity corresponding to the longest periodicity of the photonic crystal layer  420 , may be 300 to 3,000 nm. 
     The periodicity of the second photonic crystal  422  corresponding to the shortest periodicity of the photonic crystal layer  420  may be 50 to 1,000 nm. The depth of a pattern forming the second photonic crystal  422 , which has a periodicity corresponding to the shortest periodicity of the photonic crystal layer  420 , may be 50 to 500 nm. 
     Meanwhile, when it is assumed that the periodicity of the photonic crystal layer  420  is “a”, the depth of holes forming the photonic crystals of the photonic crystal layer  420  may be 0.1a to 0.45a. 
       FIG. 44  illustrates a structure of the periodicity-mixed photonic crystal layer  420  formed over the semiconductor layer  410 , in which the second photonic crystal  422 , which has a relatively short periodicity, in accordance with an etching process, and then the first photonic crystal  421 , which has a relatively long periodicity, is formed in accordance with an etching process. 
     Alternatively, as shown in  FIG. 45 , the first photonic crystal  421 , which has a relatively long periodicity, may be first formed in accordance with an etching process, and then the second photonic crystal  422 , which has a relatively short periodicity, may be formed in accordance with a deposition process. 
     When the second photonic crystal  422  is formed in accordance with a deposition process, it has a pattern of particles  422   a  protruded from the structure of the first photonic crystal  421 , in place of an engraving pattern. The particles  422   a  may have a hemispherical shape. The particles  422   a  may also have a hexagonal structure in accordance with the shape of GaN crystals. 
     When the short-periodicity second photonic crystal  422  is formed after the formation of the long-periodicity first photonic crystal  421 , as described above, the second photonic crystal  422  is also formed in holes  421   a  forming the first photonic crystal  421 . Thus, the second crystal  422  can be present in the overall portion of the light emitting surface. 
       FIG. 46  illustrates a structure in which the second photonic crystal  422 , which has a relatively short periodicity, in accordance with a deposition process, and then the first photonic crystal  421 , which has a relatively long periodicity, is formed in accordance with an etching process. 
     Since the above-described periodicity-mixed photonic crystal layer  420  has a structure including photonic crystals  421  and  422  having different periodicities, various periodicity-mixed structures may be conceived for the photonic crystal layer  420  in accordance with various combinations of the structural factors of the photonic crystals  421  and  422 . 
     Basically, the extraction efficiency depends on a combination of the periodicities of the two photonic crystals  421  and  422 . In this case, the etching depth, photonic crystal shape, etc. may function as parameters. When a new material is introduced due to the deposition process, the refractive index of the introduced material may also function as a parameter. 
     When a photonic crystal is introduced into an n-type GaN semiconductor layer in a vertical GaN-based light emitting device, for an enhancement in external extraction efficiency, it is possible to secure a maximum extraction efficiency in a long-periodicity structure (1 μm), which is easily manufactured, by deeply etching the photonic crystal in accordance with the present invention. 
     In accordance with the present invention, it is possible to maximize the extraction efficiency enhancement by providing a periodicity-mixed photonic crystal structure, in which two or more periodicities are mixed on the same plane, as an extension from a photonic crystal structure having a single periodicity. 
       FIG. 47  illustrates the structure of a vertical light emitting device which includes the above-described periodicity-mixed photonic crystal layer  420 . 
     The semiconductor layer  410 , in which the above-described photonic crystal structure is formed, includes an n-type semiconductor layer  411 , a light emitting layer  412 , and a p-type semiconductor layer  413  which are arranged in this order. As described above, the photonic crystal layer  420  is formed on the n-type semiconductor layer  411 . 
     An ohmic electrode layer or reflective ohmic electrode layer  430  may be arranged beneath the semiconductor layer  410 . The above-described light emitting device structure may be arranged on a support layer  440  made of a semiconductor such as silicon or a metal. 
     An n-type electrode  500  may be arranged on the n-type semiconductor layer  411  formed with the photonic crystal layer  420 . 
     The above-described structure has a feature in that the photonic crystal has no or little effect to cause an increase in resistance in the semiconductor layer  410  because it is formed in accordance with etching of the n-type GaN semiconductor layer  411 . Also, the light extraction effect obtained in accordance with the introduction of the photonic crystal layer  420  can be equally maintained even in a high-power output region because the vertical GaN-based light emitting device can easily discharge heat. 
     Meanwhile, since the thickness of the n-type GaN semiconductor layer  411  can generally be larger than 3 μm, the etching depth of the photonic crystal can be increased to be considerably larger than the etching depth at which the extraction efficiency is saturated. 
     As the etching depth of the photonic crystal increases as described above, the periodicity capable of securing a maximum extraction efficiency is shifted in a longer-periodicity direction. In particular, the photonic crystal, which has a periodicity of 1 μm or more, can continuously increase the extraction efficiency for an etching depth larger than an etching depth at which the extraction efficiency is saturated when a photonic crystal having a shorter periodicity is used. 
     Meanwhile, the structure of the periodicity-mixed photonic crystal layer  420 , in which different periodicities are mixed in the same plane, as described above, can exhibit a superior extraction efficiency enhancement, irrespective of the combination of photonic crystals, as compared to the structure having a single periodicity. Also, the shift of the optimal periodicity depending on the etching depth and the structure of the periodicity-mixed photonic crystal layer  420  are applicable to other light emitting device structures in which the thickness of a photonic crystal forming layer is 300 nm or more. 
     Fifth Embodiment 
       FIG. 48  illustrates the structure of a light emitting device which is capable of maximizing the extraction efficiency, taking into consideration the effect of a photonic crystal exhibited when the gap between a mirror and a light emitting layer falls under a reinforced interference condition. 
     In the illustrated light emitting device structure, a reflective electrode  530  is arranged on a support layer  540 , and a semiconductor layer  510  is arranged on the reflective electrode  530 . For the reflective electrode  530 , a material capable of making an ohmic contact with the semiconductor layer  510  may be used. Preferably, the reflective electrode  530  has a reflectance of 50% or more. 
     As shown in  FIG. 49 , a separate ohmic electrode  531  may be interposed between the reflective electrode  530  and the semiconductor layer  510 . In this case, for the ohmic electrode  531 , a transparent electrode may be used. For the transparent electrode, indium tin oxide (ITO) having a low refractive index may be used. Also, indium zinc oxide (IZO), aluminum zinc oxide (AZO), magnesium zinc oxide (MZO), or gallium zinc oxide (GZO) may be used. 
     As shown in  FIG. 48 or 49 , the semiconductor layer  510  includes a p-type semiconductor layer  513 , a light emitting layer  512  arranged on the p-type semiconductor layer  513 , and an n-type semiconductor layer  511  arranged on the light emitting layer  512 . 
     A photonic crystal  520 , which consists of a pattern including a plurality of holes  521  or rods, may be arranged on the n-type semiconductor layer  511 . An n-type electrode  550  is arranged on a portion of the n-type semiconductor layer  511 . The pattern of the photonic crystal  520  may not be formed on a region where the n-type electrode  550  is arranged. 
     In the photonic crystal  520 , the depth of each hole  521  or the height of each rod may be 300 to 3,000 nm. The photonic crystal  520  may have a periodicity of 0.8 to 5 μm. When it is assumed that the periodicity of the photonic crystal  520  is “a”, the size (diameter) of each hole  521  or each rod may be 0.25 to 0.45a. 
     As described above, the distance “d” between the reflective electrode  530  and the center of the light emitting layer  512  may be 0.65λ/n to 0.85λ/n, or may be an odd multiple of λ/4n. 
     The distance between the reflective electrode  530  and the light emitting layer  512  may be adjusted consequently by the p-type semiconductor layer  513 . That is, it is possible to establish a reinforced interference condition in a light extraction procedure by adjusting the distance between the reflective electrode  530  and the light emitting layer  512 . 
     When a separate transparent ohmic electrode  531  made of a material such as ITO is interposed between the reflective electrode  530  and the light emitting layer  512 , it is possible to more easily carry out the procedure for adjusting the thickness of the p-type semiconductor layer  513  to fall under the reinforced interference condition. 
       FIG. 50  depicts the extraction efficiency depending on the thickness of the ohmic electrode  531  when ITO is used for the ohmic electrode  531  in the structure of  FIG. 49 , using a graph.  FIG. 51  depicts a variation in extraction efficiency depending on a variation in the thickness of the p-type semiconductor layer  513  in the structure of  FIG. 49 . 
     Referring to  FIGS. 50 and 51 , it can be seen that the extraction efficiency control can be more easily achieved by adjusting the thickness of the transparent ohmic electrode  531 . This means that it is possible to more easily adjust the reinforced interference condition for light extraction by controlling the thickness of the ohmic electrode  531 . 
     In accordance with the present invention, when the photonic crystal  520  is introduced into the n-type semiconductor layer  511  of the vertical GaN-based light emitting device, in order to achieve an enhancement in external extraction efficiency, it is possible to obtain a maximum extraction efficiency under the condition in which the photonic crystal  520  has a long periodicity (1 μm or more) such that it is easily manufactured, using the interference effect of the reflective electrode  530  and the etching depth. Also, it is possible to obtain an enhancement in extraction efficiency, using only the interference effect of the reflective electrode  530 . 
     When the above-described light emitting device structure is packaged, it can exhibit a high extraction efficiency, irrespective of the structure of the package. 
       FIG. 52  illustrates a package structure in which leads  561  are formed around a package body  560 , and a light emitting device  500  having the above-described features is mounted on the top of the package body  560 . The light emitting device  500  may be connected to the leads  561  via wires  562 . A zener diode  570  is arranged at one side of the light emitting device  500 , to achieve an improvement in withstanding voltage characteristics. 
     The package body  560 , on which the light emitting device  500  is mounted, is encapsulated with a planar encapsulate. 
       FIG. 53  illustrates a structure in which the light emitting device  500  is mounted on a package body  580 , and a dome-shaped encapsulate  590  is formed. 
     Light emitted from the above-described light emitting device  500  while having a strong directionality in a vertical direction can exhibit substantially-equal power characteristics in the planar package structure of  FIG. 52  and the dome-shaped package structure of  FIG. 53 . 
     Sixth Embodiment 
     Hereinafter, a procedure for manufacturing a light emitting device having a light extracting structure, such as a photonic crystal, in accordance with the present invention will be described. 
       FIG. 54  illustrates an LED structure  600  formed on a substrate  610 . 
     For the formation of the LED structure  600 , a compound semiconductor layer  620  is first formed over the substrate  610  which is made of, for example, sapphire. The semiconductor layer  620  includes an n-type semiconductor layer  621 , an active layer  622 , and a p-type semiconductor layer  623  which are arranged, in this order, starting from the side of the substrate  610 . 
     The arrangement order of the n-type semiconductor layer  621 , active layer  622 , and p-type semiconductor layer  623  may be reversed. That is, these layers may be formed over the substrate  610  in the order of the p-type semiconductor layer  623 , the active layer  622 , and the n-type semiconductor layer  621 . 
     In particular, for the semiconductor layer  620 , a GaN-based semiconductor may be used. In this case, the active layer  622  may have an InGaN/GaN quantum well (QW) structure. Also, a material such as AlGaN or AlInGaN may be used for the active layer  622 . when an electric field is applied to the active layer  622 , light is generated in accordance with coupling of electron-hole pairs. 
     In order to achieve an enhancement in brightness, the active layer  622  may have a multi-quantum well (MQW) structure including a plurality of QW structures as described above. 
     A p-type electrode  630  is formed over the semiconductor layer  620 . The p-type electrode  630  is an ohmic electrode. A reflective electrode  640  may be formed over the p-type electrode  630 , to reflect light generated from the active layer  622 , and thus, to externally emit the generated light. 
     In place of the p-type electrode  630  and reflective electrode  640 , a single electrode may be formed by appropriately selecting the materials of the p-type electrode  630  and reflective material  640 , to function as both the p-type electrode  630  and the reflective electrode  640 . 
     A support layer  650  may be formed over the reflective electrode  640 , to support the LED structure  600  in a subsequent procedure for separating the substrate  610 . 
     The support layer  650  may be formed by bonding a semiconductor substrate made of silicon (Si), gallium arsenide (GaAs), or germanium (Ge) or a metal substrate made of CuW to an upper surface of the reflective electrode  640 . Alternatively, the support layer  650  may be formed by plating a metal such as nickel (Ni) or copper (Cu) over the reflective electrode  640 . 
     Where the support layer  650  is made of a metal, it may be formed using a seed metal, in order to enhance the bondability to the reflective electrode  640 . 
     In accordance with the above-described processes, the LED structure  600  has a structure as shown in  FIG. 54 . From this structure, the substrate  610  is then removed. Thereafter, a dielectric layer  660  is formed over the surface, from which the substrate  610  has been removed. Thus, a structure as shown in  FIG. 55  is obtained. 
     The removal of the substrate  610  may be achieved in accordance with a laser lift-off process using a laser. Alternatively, the substrate  610  may be removed in accordance with a chemical method such as an etching method. 
     During the procedure for removing the substrate  610 , the support layer  650  supports the LED structure  600 . 
     As described above, the dielectric layer  660  is formed over the n-type semiconductor layer  621  exposed in accordance with the removal of the substrate  610 . For the dielectric layer  660 , an oxide or a nitride may be used. For example, a silicon oxide (SiO 2 ) may be used. 
     A plurality of regular holes  661  are formed in the dielectric layer  660 . The formation of the holes  661  may be achieved using a dry etching process such as a reactive ion etching (RIE) process or an inductively-coupled plasma reactive ion etching (ICP-RIE) process. 
     The dry etching process is suitable for the formation of the holes  661  because uni-directional etching can be achieved, different from a wet etching process. That is, although isotropic etching is carried out in the wet etching process such that etching is achieved in all directions, etching only in a depth direction for formation of the holes  661  can be achieved in accordance with the dry etching process. Accordingly, the holes  661  can be formed to have a desired pattern in terms of size and spacing, in accordance with the dry etching process. 
     In order to form the multiple holes  661  as described above, a pattern mask  670  formed with a hole pattern  671  as shown in  FIG. 56  may be used. 
     For the pattern mask  670 , a metal mask made of, for example, chromium (Cr), may be used. If necessary, photoresist may be used. 
     Where photoresist is used for the pattern mask  670 , the hole pattern  671  may be formed using a photolithography, an e-beam lithography, nano-imprinted lithography, or the like. In this procedure, a dry etching process or a wet etching process may be used. 
     Where a chromium mask is used for the pattern mask  670 , a polymer layer is first formed a chromium layer, to form a pattern on the chromium layer. A pattern is then formed over the polymer layer in accordance with an imprinting method. Thereafter, the chromium layer is etched. Thus, the pattern mask  670  is formed. The etching of the chromium layer is achieved using a dry etching process. 
     For the dry etching process, an RIE process or an ICP-RIE process may be used. For the gas used in this process, at least one of Cl 2  and O 2  may be used. 
     Preferably, the hole pattern  671  is not formed in a certain region, to provide an empty space where n-type electrode pads  691  ( FIG. 66 ) will be formed. 
     Through the above-described procedure, a plurality of holes  661  having the same pattern as the hole pattern  671  are formed in the dielectric layer  660 , as shown in  FIG. 57 . In this case, the holes  661  extend throughout the dielectric layer  660 . 
     The holes  661  may have various patterns. For example, the holes  661  have a square pattern. Also, the holes  661  may have various patterns as shown in  FIGS. 58 to 62 . 
     That is, the holes  661  are formed to be arranged along oblique lines defined in a light emitting device package, as show in  FIG. 58 . Also, the holes  661  may be formed to be arranged along oblique lines defined in a plurality of divided surface regions in a light emitting device package, as shown in  FIG. 59 . In this case, the oblique-line pattern of each surface region may not meet those of the remaining surface regions. 
     Alternatively, the oblique-line pattern of each region may meet those of the remaining regions, as shown in  FIGS. 60 and 61 .  FIG. 60  illustrates the case in which the holes  661  are arranged along oblique lines defined in two divided regions of a light emitting device such that the oblique-line patterns meet at the boundary of the regions.  FIG. 61  illustrates the case in which the holes  661  are arranged along oblique lines defined in four divided regions of a light emitting device such that the oblique-line patterns meet at the boundaries of the regions. 
     On the other hand, as shown in  FIG. 62 , the holes  661  may be arranged to form a plurality of concentric circle patterns or radial patterns. 
     In addition, the holes  661  may have various polygonal patterns such as hexagonal patterns or octagonal patterns, or trapezoidal patterns. Also, an irregular pattern may be formed. 
     After the formation of the hole  661  in the dielectric layer  660  arranged on the n-type semiconductor layer  621 , etching is carried out for the n-type semiconductor layer  621  in accordance with a dry etching process, to form a plurality of grooves  624 , as shown in  FIG. 58 . 
     Thus, the dielectric layer  660  formed over the n-type semiconductor layer  621  functions as a mask or a passivation film for etching the n-type semiconductor layer  621 . 
     In this case, the grooves  624  are formed to have the same pattern as the holes  661 . 
     That is, the grooves  624  may be formed to have a pattern such as a square pattern, a plurality of oblique-line patterns, a plurality of oblique-line patterns divided into at least two regions, a plurality of oblique-line patterns divided into at least two regions while extending in opposite directions, a plurality of concentric patterns, polygonal patterns, trapezoidal patterns, or radial patterns 
       FIG. 63  illustrates a procedure for forming the grooves  624  in the n-type semiconductor layer  621 , using an ICP-RIE apparatus. 
     For the ICP-RIE apparatus, a planar type or a solenoid type may be used. In  FIG. 63 , a planar type ICP-RIE apparatus is illustrated. 
     In the ICP-RIE apparatus, a copper coil  710  is arranged on a chamber  700  including a grounded metal shield  701  and an insulating window  702  covering the metal shield  701 . Electric power from a radio-frequency (RF) power supplier  720  is applied to the coil  710 . In this case, an electric field should be formed at an appropriate angle, in order to insulate the insulating window  702  by the RF power. 
     The LED structure  600  formed with the dielectric layer  660  with the pattern of holes  661  is laid on a lower electrode  730  arranged in the chamber  700 . The lower electrode  730  is connected to a bias voltage supplier  740  for supplying a bias voltage to bias the LED structure  600  such that desired etching is achieved. 
     The bias voltage supplier  740  preferably supplies RF power and a DC bias voltage. 
     A gas mixture including at least one of Ar, BCl 3 , and Cl 2  is introduced into the chamber  700  through a reactive gas port  703 . At this time, electrons are injected into the chamber  700  through a top port  704 . 
     The injected electrons strike neutral particles of the introduced gas mixture due to an electromagnetic field generated by the coil  710 , thereby generating ions and neutral atoms to produce plasma. 
     The ions in the plasma are accelerated to move toward the LED structure  600 , by the bias voltage from the bias voltage supplier  740  supplied to the electrode  730 . The accelerated ions pass through the pattern of the holes  661  of the dielectric layer  660 , together with the accelerated electrons, thereby forming the pattern of the grooves  624  in the n-type semiconductor layer  621 , as shown in  FIG. 64 . 
     In this case, the pressure of the chamber  700  is maintained at 5 mTorr. An He flow may also be used. Preferably, the chamber  700  is cooled to 10° C. during the etching procedure. 
     For the RF power supplier  720  and bias voltage supplier  740 , electric power of 33 W and 230 W may be used, respectively. 
     For the formation of the holes  660  in the dielectric layer  661 , the above-described ICP-RIE apparatus may also be used in the same manner as described above. In this case, the gas mixture may include at least one of CF 4 , Ar, and CHF 3 . The RF power supplier  720  and bias voltage supplier  740  may use electric power of 50 W and 300 W, respectively. 
     The holes  660  may be irregularly formed in the dielectric layer  661  in the above-described procedure, to irregularly form the grooves  624  in the n-type semiconductor layer  621 . The irregular grooves  624  provide a rough surface, through which light is extracted, to achieve an enhancement in extraction efficiency. 
     However, it is preferred that the pattern of the grooves  624  be regular to have a certain periodicity ( FIGS. 58 to 62 ), and thus, to form a photonic crystal structure  680  on the surface of the n-type semiconductor layer  621 . 
       FIG. 65  illustrates a scanning electron microscope (SEM) image of the photonic crystal structure  680  formed on the n-type semiconductor layer  621  in accordance with the above-described procedures. 
     The photonic crystal structure  680  is formed such that the periodicity of a photonic crystal is 0.5 to 1.5 μm, and the diameter of the grooves  624  forming the photonic crystal corresponds to about 0.3 to 0.6 times the photonic crystal periodicity, taking into consideration the refractive index of GaN (2.6), the refractive index of an epoxy lens, which is included in the LED structure and from which light is extracted, (1.5), and the relation with a driving voltage. 
     The grooves  624  may have a depth corresponding to ⅓ or more of the thickness of the n-type semiconductor layer  621 . 
     When the above-described photonic crystal structure  680  is formed, it has a periodic refractive index arrangement. When the periodicity of the photonic crystal structure  680  corresponds to about half of the wavelength of emitted light, a photonic band-gap is formed in accordance with multi-scattering of photons by a photonic crystal lattice having a periodic variation in refractive index. 
     In the photonic crystal structure  680 , light has a property of effective emission in a certain direction. That is, a light prohibition zone is formed. Accordingly, there may be a phenomenon that light is extracted through regions other than the holes  624  forming the phonic crystal structure  680  without entering or passing through the holes  624 . 
     As described above, the n-type electrode pads  691  and p-type electrode pads  692  are formed at upper and lower surfaces of the LED structure  600  formed with the photonic crystal structure  680 , as shown in  FIG. 66 . Thus, the LED structure  600  is completely manufactured. 
     It will be apparent to those skilled in the art that various modifications and variations can be made in the present invention without departing from the spirit or scope of the inventions. Thus, it is intended that the present invention covers the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.