Patent Publication Number: US-2013248912-A1

Title: Semiconductor light emitting element

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2012-070227, filed on Mar. 26, 2012; the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments described herein relate generally to a semiconductor light emitting element. 
     BACKGROUND 
     It is required for semiconductor light emitting elements to have high brightness properties in order to improve visibility and efficiency. In the semiconductor light emitting element, high brightness properties are achieved by forming a concavoconvex structure on a main light extraction surface. In such a concavoconvex structure, an optical phenomenon depending on the concavoconvex period with respect to the wavelength of light may occur. 
     When light is applied to a light extraction surface having a concavoconvex structure with a period much larger than the wavelength of the light, the light acts pursuant to geometrical-optical behavior. In the case where a concavo-convex structure with a period of approximately one to several times the wavelength of light is formed on the light extraction surface, the light is diffracted. In the case where a concavo-convex structure with a period sufficiently smaller than the wavelength of light is formed on the light extraction surface, a GI (graded index) structure is produced in which the average refractive index continuously changes from the interior of a substrate toward the outside in a range of approximately the wavelength of the light. Consequently, Fresnel reflection within the critical angle is reduced. 
     In such a semiconductor light emitting element, it is desired to further improve the light extraction efficiency. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic view illustrating a configuration of a semiconductor light emitting element according to a first embodiment; 
         FIGS. 2A and 2B  are diagrams illustrating a transmittance of light in a case of having a concavoconvex structure; 
         FIGS. 3A and 3B  are diagrams illustrating a transmittance of light of the semiconductor light emitting element according to the embodiment; 
         FIGS. 4A and 4B  are schematic diagrams showing effects of an optical layer; 
         FIGS. 5A and 5B  are schematic diagrams illustrating parameters of Mathematical Formula; 
         FIG. 6  is a schematic diagram illustrating a configuration of a measurement apparatus of a light extraction efficiency; 
         FIG. 7  is a diagram showing a relationship between a first region and a refractive index; 
         FIG. 8  is a diagram illustrating simulation results showing a relationship between a wavelength and a light transmittance; 
         FIG. 9  to  FIG. 11  are diagrams illustrating simulation results of a direction of scattering due to a second particle; and 
         FIG. 12  to  FIG. 14  are diagrams showing simulation calculation results of light transmittance versus incident angle. 
     
    
    
     DETAILED DESCRIPTION 
     In general, according to one embodiment, a semiconductor light emitting element includes a stacked body having a major surface and including a light emitting layer and an optical layer provided in contact with the major surface of the stacked body and including a dielectric body, a plurality of first particles having a refractive index different from a refractive index of the dielectric body, and a plurality of second particles having a refractive index different from a refractive index of the dielectric body, the optical layer including a first region including the dielectric body and the plurality of first particles and not including the plurality of second particles; and a second region including the dielectric body and the plurality of second particles, a sphere-equivalent diameter of the first particle being not less than 1 nanometer and not more than 100 nanometers, a sphere-equivalent diameter of the second particle being more than 300 nanometers and less than 1000 nanometers, an average refractive index of the first region being larger than a refractive index of the stacked body and smaller than a refractive index of the second particle. 
     Hereinbelow, embodiments of the invention are described based on the drawings. 
     The drawings are schematic or conceptual; and the relationships between the thickness and width of portions, the proportions of sizes among portions, etc. are not necessarily the same as the actual values thereof. Further, the dimensions and proportions may be illustrated differently among drawings, even for identical portions. 
     In the specification of this application and the drawings, components similar to those described in regard to a drawing thereinabove are marked with the same reference numerals, and a detailed description is omitted as appropriate. 
     In the following description, as an example, specific examples are given in which the first conductivity type is the n-type and the second conductivity type is the p-type. 
     First Embodiment 
       FIG. 1  is a schematic view illustrating the configuration of a semiconductor light emitting element according to a first embodiment. 
     As shown in  FIG. 1 , a semiconductor light emitting element  110  according to the first embodiment includes a stacked body  10  and an optical layer  20 . 
     The stacked body  10  includes a first semiconductor layer  11  of a first conductivity type, a second semiconductor layer  12  of a second conductivity type, and a light emitting layer  13  provided between the first semiconductor layer  11  and the second semiconductor layer  12 . The stacked body  10  has a major surface  10   a  on the side of the second semiconductor layer  12 . In the embodiment, the direction perpendicular to the major surface  10   a  is referred to as a Z direction. 
     The first semiconductor layer  11  includes, for example, a cladding layer  11   b.  The cladding layer  11   b  is formed on a substrate  11   a.  In the embodiment, for the sake of convenience, it is assumed that the substrate  11   a  is included in the first semiconductor layer  11 . 
     The second semiconductor layer  12  includes, for example, a cladding layer  12   a . A current spreading layer  12   b , for example, is provided on the cladding layer  12   a , and a contact layer  12   c  is provided thereon. In the embodiment, for the sake of convenience, it is assumed that the current spreading layer  12   b  and the contact layer  12   c  are included in the second semiconductor layer  12 . 
     The light emitting layer  13  is provided between the first semiconductor layer  11  and the second semiconductor layer  12 . In the semiconductor light emitting element  110 , for example, a hetero-structure is formed by the cladding layer  12   b  of the first semiconductor layer  11 , the light emitting layer  13 , and the cladding layer  12   a  of the second semiconductor layer  12 . 
     The light emitting layer  13  may be, for example, an MQW (multiple quantum well) configuration in which barrier layers and well layers are alternately provided in a repeated manner. The light emitting layer  13  may be what includes an SQW (single quantum well) configuration in which one set of a well layer and barrier layers sandwiching the well layer is provided. 
     A not-shown electrode is provided to each of the first semiconductor layer  11  and the second semiconductor layer  12 . By applying a prescribed voltage between the first semiconductor layer  11  and the second semiconductor layer  12 , light having a prescribed center wavelength (e.g. a wavelength of visible light) is emitted from the light emitting layer  13 . The light is mainly emitted from the major surface  10   a  to the outside. That is, the major surface  10   a  is one of the main light extraction surfaces of the semiconductor light emitting element  110 . 
     The optical layer  20  is provided in contact with the major surface  10   a  of the stacked body  10 . 
     The optical layer  20  includes a dielectric body  21 , a plurality of first particles  22 , and a plurality of second particles  23 . The refractive index of the plurality of first particles  22  is different from the refractive index of the dielectric body  21 . The refractive index of the plurality of second particles  23  is different from the refractive index of the dielectric body  21 . In the embodiment, the refractive index is the refractive index for the wavelength of the light emitted from the light emitting layer  13  unless otherwise specified. 
     The optical layer  20  includes a first region R 1  and a second region R 2 . 
     The first region R 1  is a region that includes the dielectric body  21  and a plurality of first particles  22  and does not include a plurality of second particles  23 . The second region R 2  is a region that includes the dielectric body  21  and a plurality of second particles  23 . 
     At least one selected from silicon oxide, an epoxy resin, and a silicone resin is used for the dielectric body  21 . The first particle  22  and the second particle  23  are dielectric materials, and an oxide or a nitride of at least one selected from the group consisting of titanium, zinc, tin, indium, zirconium, silicon, and tungsten or polystyrene is used therefor. 
     In the semiconductor light emitting element  110  according to the embodiment, the sphere-equivalent diameter of the first particle  22  is not less than 1 nanometer and not more than 100 nanometers. The sphere-equivalent diameter of the second particle  23  is more than 300 nanometers and less than 1000 nanometers. 
     In the embodiment, the sphere-equivalent diameter refers to the volume average diameter of spheres having an equal effect of interaction with light. 
     The sphere-equivalent diameter is directly measured with, for example, a laser particle size distribution meter. 
     In the semiconductor light emitting element  110  according to the embodiment, the average refractive index of the first region R 1  is larger than the refractive index of the stacked body  10  and smaller than the refractive index of the second particle  23 . 
     In the embodiment, the average refractive index refers to the average value of the refractive index of the dielectric body  21  and the refractive index of the first particle  22  on a volume ratio basis. 
     By the semiconductor light emitting element  110  thus configured, the extraction efficiency of light emitted from the major surface  10   a  that is one of the light extraction surfaces (light extraction efficiency) is improved. 
     In the embodiment, the light extraction efficiency refers to the proportion of the intensity of light that can be extracted to the outside of the semiconductor light emitting element  110  to the intensity of the light generated in the light emitting layer. 
     Next, the transmittance of light is described. 
       FIGS. 2A and 2B  are diagrams illustrating the transmittance of light in the case of having a concavo-convex structure. 
       FIG. 2A  is a schematic cross-sectional view illustrating a concavo-convex structure, and  FIG. 2B  is a diagram illustrating the transmittance T versus the incident angle θc. 
     As shown in  FIG. 2A , in the case where a concave-convex  15  is provided at the major surface  10   a  of the stacked body  10 , the transmittance T of light emitted from the interior of the stacked body  10  to the outside via the concave-convex  15  changes with the pitch Pt of the concave-convex  15 . 
     When the light traveling from the interior of the stacked body  10  toward the major surface  10   a  is denoted by C 1  and the light emitted from the major surface  10   a  (the concave-convex  15 ) to the outside is denoted by C 2 , the light transmittance T is expressed by the intensity of C 2 /the intensity of C 1 . The incident angle of the light C 1  with respect to the axis perpendicular to the major surface  10   a  is referred to as an incident angle θc. 
       FIG. 2B  shows examples of the light transmittance T versus the incident angle θc of semiconductor light emitting elements  190 ,  191 , and  192 . Here, the semiconductor light emitting element  190  has a structure in which the concave-convex  15  is not provided at the major surface  10   a,  the semiconductor light emitting element  191  has a structure in which the concave-convex  15  with a relatively small pitch Pt is provided at the major surface  10   a,  and the semiconductor light emitting element  192  has a structure in which the concave-convex  15  with a relatively large pitch Pt is provided at the major surface  10   a.    
     The stacked body  10  of the semiconductor light emitting element generally has a high refractive index. Therefore, in the semiconductor light emitting element  190  having a flat light extraction surface, light of not less than the critical angle depending on the refractive index of the stacked body  10  included in the semiconductor light emitting element  190  is totally reflected at the light extraction surface (the major surface  10   a ). Consequently, only part of the light generated in the light emitting layer is emitted to the outside of the semiconductor light emitting element  190 . 
     In the semiconductor light emitting element  191  including the concave-convex  15  with a pitch Pt much smaller than the wavelength of light, a GI structure is produced in which the average refractive index in a range of approximately the wavelength of the light C 1  continuously changes from the interior of the stacked body  10  toward the outside. Therefore, Fresnel reflection within the critical angle is reduced as compared to the semiconductor light emitting element  190 , and the light transmittance T within the critical angle is improved. 
     In the semiconductor light emitting element  192  including the concave-convex  15  with a pitch Pt much larger than the wavelength of light, the light C 1  acts pursuant to geometrical-optical behavior. In the semiconductor light emitting element  192  including such a concave-convex  15 , even when light C 1  of not less than the critical angle with respect to the light extraction surface (the major surface  10   a ) is caused to be incident, the light C 1  is transmitted without being totally reflected as long as the light C 1  has an incident angle of not more than the critical angle with respect to the surface of the concave-convex  15  provided. Thus, light T in the range exceeding the critical angle is increased as compared to the semiconductor light emitting elements  190  and  191 . 
     Here, in the semiconductor light emitting elements  191  and  192  in which a periodic concavo-convex structure is formed at the light extraction surface (the major surface  10   a ), since an optical phenomenon corresponding to the pitch Pt of the concave-convex  15  is utilized, the proportion between the light transmittance T within the critical angle and the light transmittance T of not less than the critical angle depends on the pitch Pt of the concave-convex  15 . Therefore, it is not possible to obtain a light extraction efficiency of a certain proportion or more to the light extraction efficiency in the semiconductor light emitting element  190  having a flat light extraction surface. 
       FIGS. 3A and 3B  are diagrams illustrating the transmittance of light of the semiconductor light emitting element according to the embodiment. 
       FIG. 3A  is a schematic enlarged cross-sectional view of a portion in and around the optical layer, and  FIG. 3B  is a diagram illustrating the transmittance T versus the incident angle θc. 
     As shown in  FIG. 3A , the optical layer  20  of the semiconductor light emitting element  110  according to the embodiment includes the first region R 1  and the second region R 2 . The first region R 1  is a region in which a plurality of first particles  22  are contained in the dielectric body  21  and the second particle  23  is not contained. The second region R 2  is a region in which a plurality of second particles  23  are contained in the dielectric body  21 . First particles  22  may be contained in the second region R 2 . 
     The distribution (the frequency to the particle size) of the particle size (the sphere-equivalent diameter) of the particles included in the optical layer  20  has a plurality of peaks. The first particle  22  and the second particle  23  are included in a distribution with center at two peaks on the higher frequency side out of the plurality of peaks. 
     In the particle size distribution of the particles included in the optical layer  20 , the peak of the sphere-equivalent diameter of the first particle  22  is in a range of not less than 1 nm and not more than 100 nm, and the peak of the sphere-equivalent diameter of the second particle  23  is in a range of more than 300 nm and less than 1000 nm. 
     The first region R 1  including the first particle  22  provides a reflection prevention effect in the case where the incident angle θc is small (e.g. not more than the critical angle), and the second region R 2  including the second particle  23  provides diffraction and scattering effects in the case where the incident angle θc is large (e.g. not less than the critical angle). 
     Here, if the particle size of the first particle  22  is too small, unintentional mixing-in occurs because of the excessively small particle size, and the characteristics of the objective cannot be obtained. Conversely, if the particle size of the first particle  22  is too large, the effect of the second particle  23  appears because of the proximity to the particle size of the second particle  23 , and it is difficult to obtain the effect of particle separation. 
     If the particle size of the second particle  23  is too small, the effect of the first particle  22  appears because of the proximity to the particle size of the first particle  22 , and it is difficult to obtain the effect of particle separation. Conversely, if the particle size of the second particle  23  is too large, it is difficult to obtain a scattering effect. 
     The sphere-equivalent diameter of the first particle  22  is preferably not less than 1 nm and not more than 70 nm. The sphere-equivalent diameter of the second particle  23  is preferably not less than 300 nm and not more than 700 nm, and more preferably not less than 400 nm and not more than 700 nm. 
     The sphere-equivalent diameter of the first particle  22  is 1/10 or less of the wavelength of the light emitted from the light emitting layer  13 , and preferably 1/20 or less. The sphere-equivalent diameter of the second particle  23  is equal to the wavelength of the light emitted from the light emitting layer  13 . Here, “equal to the wavelength” includes not only the case of being exactly equal but also the case of being substantially equal to the wavelength (e.g. ±50% of the wavelength). 
     The thickness of the first region R 1  is preferably not less than 30 nm and not more than the thickness of the second region R 2 . This is because an excessively small thickness of the first region  22  makes it difficult to obtain the effect of reflection prevention in the first region R 1 , and conversely an excessively large thickness makes it necessary for the regions to be formed with a distinction and is industrially disadvantageous. 
     The thickness of the second region R 2  is preferably 3 times or less the average of the sphere-equivalent diameters of the plurality of second particles  23 . This is because an excessively large thickness thereof reduces the scattering effect of the second region R 2 . The thickness of the second region R 2  is preferably 1.5 times or less the average of the sphere-equivalent diameters of the plurality of second particles  23 . This is because the effect expected tends to be reduced as second particles  23  become more multiple layers. 
     In addition, when the absolute refractive index of the first region R 1  is denoted by n, the average thickness of the first region R 1  is denoted by d (nm), the wavelength of the light passing through the first region is denoted by λ (nm), and m is an integer of 0 or more, Mathematical Formula 1 is preferably satisfied. 
       (0.15+ m/ 2)×λ≦ nd≦( 0.35+ m/ 2)×λ  [Mathematical Formula 1]
 
     In the semiconductor light emitting element  110  according to the embodiment, characteristics of the transmittance T like those shown in  FIG. 3B  are obtained by providing the optical layer  20  including the first particle  22  and the second particle  23  like the above. That is, in the semiconductor light emitting element  110  according to the embodiment, the first region R 1  including the first particle  22  provides a reflection prevention effect in the case where the incident angle θc is small (e.g. not more than the critical angle), and the second region R 2  including the second particle  23  provides diffraction and scattering effects in the case where the incident angle θc is large (e.g. not less than the critical angle). Thereby, a reflection prevention effect and diffraction and scattering effects that cannot be achieved by the semiconductor light emitting element including the concave-convex  15  shown in  FIGS. 2A and 2B  are obtained, and an improvement in the light extraction efficiency is achieved. 
       FIGS. 4A and 4B  are schematic diagrams showing effects of the optical layer. 
       FIG. 4A  is a schematic view showing the reflection prevention effect, and  FIG. 4B  is a schematic diagram showing the scattering effect. 
     First, the reflection prevention effect by the first region R 1  including the first particle  22  and the dielectric body  21  is described. 
     As shown in  FIG. 4A , the first region R 1  of the optical layer  20  provided on the major surface  10   a  of the stacked body  10  has a reflection prevention effect. For example, when the sphere-equivalent diameter of the first particle  22  is made approximately 1/10 or less of the wavelength or preferably smaller than approximately 1/20 of the wavelength, first particles  22  are scattered at an almost fixed intensity for all the scattering angles. 
     When first particles  22  are uniformly scattered in the dielectric body  21 , the scattered light due to first particles  22  per unit volume is equal to the sum of the light due to scattering corresponding to the number of first particles  22  scattered in a unit volume as illustrated in Mathematical Formula 2. 
         I (θ, φ)=Σ i   j (θ, φ)≈ ×n    [Mathematical Formula 2]
 
       FIGS. 5A and 5B  are schematic diagrams illustrating the parameters of Mathematical Formula 2. 
     Here, I(θ, φ) is the intensity of scattered light due to first particles  22  per unit volume in the direction of the angle (θ, φ) shown in  FIG. 5A , i j(θ, φ)  is the intensity of scattered light due to the first particle  22 ( j ) of the j-th in the direction of the angle (θ, φ) shown in  FIG. 5B , i is the intensity normalized with respect to the solid angle of scattered light due to the single first particle  22 ( j ), and n is the number of first particles  22  per unit volume. 
     As can be seen from Mathematical Formula 2, the dielectric body  21  containing very small first particles  22  with a size of approximately 1/10 of the wavelength of the light transmitted does not act as a scatterer having an angle dependence. 
     Next, the optical behavior of the dielectric body  21  containing very small first particles  22  with a size of approximately 1/10 of the wavelength of the light transmitted is described. Maxwell-Garnett has revealed that the effective dielectric constant of a complex (the first region R 1 ) including the first particle  22  and the dielectric body  21  changes in accordance with the relationship of Mathematical Formula 3. 
     
       
         
           
             
               
                 
                   
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     Further, the refractive index is expressed by Mathematical Formula 4 from the dielectric constant. 
       n eff =√{square root over (ε eff )}  [Mathematical Formula 4]
 
     where ε eff  is the effective dielectric constant of the complex (the first region R 1 ) including the first particle  22  and the dielectric body  21 , ε p  is the dielectric constant of the first particle  22 , ε m  is the dielectric constant of the dielectric body  21 , d is the volume fraction of first particles  22  in the complex (the first region R 1 ) including the first particle  22  and the dielectric body  21 , and n eff  is the effective refractive index of the complex (the first region R 1 ) including the first particle  22  and the dielectric body  21 . 
     Thus, the first region R 1  acts as a medium having a refractive index (an average refractive index) obtained by averaging the refractive index of the dielectric body  21  and the refractive index of the first particle  22  on a volume ratio basis. 
     By setting the average refractive index of the first region R 1  to a value between the refractive index of the stacked body  10  and the refractive index of the outside (e.g. the refractive index of air,  1 ), the reflection at the major surface  10   a  of the light traveling from the interior of the stacked body  10  toward the outside is reduced. Consequently, the transmittance T of light is improved. 
     In the case where, as an example, GaP (refractive index: 3.2) is use for the stacked body  10 , SiO 2  (refractive index: 1.45) is used for the dielectric body  21 , TiO 2  (refractive index: 2.5) is used for the first particle  22 , and the volume ratio between the first particle  22  and the dielectric body  21  is set to 1:1, the average refractive index is approximately 2.0. 
     The transmittance T of light from the stacked body  10  to the outside in the case of including the optical layer  20  thus configured is 16×2.0 2 ×3.2/(1+2.0) 2 ×(2.0+3.2) 2 =84%. 
     On the other hand, the transmittance T of light from the stacked body  10  to the outside in the case of not including the optical layer  20  is 4×3.2/(1+3.2) 2 =73%. 
     Here, when the thickness (the thickness with the major surface  10   a  as a reference) t 1  (see  FIG. 3A ) of the first region R 1  is set to the condition expressed by Mathematical Formula 1, the light reflected from the first region R 1  to the interior of the stacked body  10  is canceled. Consequently, the quantity of light transmitted from the first region R 1  to the external medium is increased. Thereby, at the major surface  10   a  that is a light extraction surface of the semiconductor light emitting element  110 , Fresnel reflection within the critical angle is reduced, and the transmittance T of light emitted frontward is improved. 
     Due to the change in the effective refractive index of the first region R 1 , also the scattering intensity of light due to the second particle  23  changes. 
     Thus, in the semiconductor light emitting element  110  of the embodiment, the first region R 1  of the optical layer  20  provides a reflection prevention effect to improve the transmittance T of light. 
     The average refractive index of the first region R 1  is adjusted by the volume ratio between the dielectric body  21  and the first particle  22 . Thus, the average refractive index is adjusted by the volume ratio of first particles  22  without changing the material of the dielectric body  21  and the material of the first particle  22 . 
     In the embodiment, the average refractive index of the first region R 1  is finely set by the volume ratio of first particles  22  based on the refractive index of the material of the stacked body  10 , the refractive index of the material of the second particle  23  included in the second region R 2 , etc. 
     Thereby, even when the refractive index cannot be adjusted by alterations of the materials of the dielectric body  21  and the first particle  22 , an optimum refractive index is selected by the volume ratio of first particles  22 , and an improvement in the light extraction efficiency by a reflection prevention effect is achieved. 
     Next, the light scattering and diffraction effects by the second region R 2  including the second particle  23  and the dielectric body  21  are described. 
     As shown in  FIG. 4B , the second particle  23  included in the second region R 2  of the optical layer  20  provided on the major surface  10   a  of the stacked body  10  exhibits a light scattering effect. For example, when light C is incident on the second particle  23  having a sphere-equivalent diameter approximately equal to the wavelength, polarization occurs in the second particle  23 . The light C is scattered by the polarization. 
     When light having a wavelength approximately equal to the sphere-equivalent diameter is caused to be incident on a single second particle  23 , the light is scattered with an angle dependence. The light scattered changes with the wavelength of the light, the size of the second particle  23 , and the absolute value of the difference between the refractive index of the second particle  23  and the refractive index of the dielectric body  21 . In other words, the second particle  23  with a sphere-equivalent diameter of approximately one to several times the wavelength of the light transmitted has a refractive index different from the effective refractive index of the complex (the first region R 1 ) including the first particle  22  and the dielectric body  21  described above; thereby, a scattering phenomenon occurs. 
     At this time, at the single second particle  23 , the intensity of forward scattering of the scattered light is smaller than 1/100 of the intensity of backward scattering. Thus, light loss at not less than the critical angle at the major surface  10   a  that is a light extraction surface is reduced. 
     In view of the fact that the refractive index of the dielectric body  21  that is a scattering medium used is larger than the refractive index of air, forward scattering is sufficiently great when the sphere-equivalent diameter of the second particle  23  is larger than 300 nm. However, if the sphere-equivalent diameter of the second particle  23  is as large as several times the wavelength, a scattering having an angle dependence in accordance with the shape of the second particle  23  occurs. The sphere-equivalent diameter of the second particle  23  is preferably approximately less than 1000 nm. This is because backward scattering is strong when the sphere-equivalent diameter of the second particle  23  is 1000 nm or more. 
     Here, in the case where second particles  23  are sparse and the spacing between adjacent second particles  23  and the arrangement are random, the scattering of light due to a single second particle  23  can be regarded as occurring at each of the plurality of second particles  23 . In other words, when a large number of second particles  23  exist in the dielectric body  21 , the scattering intensity due to the second particle  23  increases with the concentration of second particles  23 . 
     On the other hand, when the concentration of second particles  23  exceeds a certain value and the distance between adjacent second particles  23  becomes short, scattered light rays interact with one another and a diffraction phenomenon is thus caused. When diffraction occurs, the scattering intensity is increased for angles satisfying diffraction. 
     An investigation by the inventors of this application has revealed that, as a condition whereby the scattering intensity is increased by diffraction, the distance (the center-of-mass distance) between adjacent second particles  23  is not less than 1.1 times and not more than 3 times the average of the sphere-equivalent diameters of the plurality of second particles  23 . 
     That is, the lower limit of the spacing between second particles  23  is approximately the most proximity. The upper limit of the spacing between second particles  23  is preferably set not more than a spacing at which the occupation area of second particles  23  is approximately 10% (not more than 3 times the average of the sphere-equivalent diameters of the plurality of second particles  23 ). Exceeding this upper limit reduces the intensity of diffracted light to result in a reduced effect. 
     The second particles  23  included in the second region R 2  are preferably three layers or less in the Z direction. When the second particles  23  are three layers or less, sufficient light by the diffraction of light is extracted to the outside. Further, to prevent the scattered light from being backward scattered, the second particles  23  are preferably one layer in the Z direction. 
     To make the second particles  23  three layers or less in the Z direction as mentioned above, the thickness (the thickness with the major surface  10   a  as a reference) t 2  (see  FIG. 3A ) of the second region R 2  is less than 3000 nm, preferably  3  times or less the average of the sphere-equivalent diameters of the plurality of second particles  23 , and more preferably 1.5 times or less. 
     To cause scattering and diffraction, the thickness t 2  of the second region R 2  is preferably not less than the thickness t 1  of the complex (the first region R 1 ) composed of the first particle  22  and the dielectric body  21 . 
     Thus, light of not less than the critical angle resulting from the refractive index of the stacked body  10  is scattered by the second particle  23  having a sphere-equivalent diameter of approximately one to several times the wavelength of the light transmitted, and light is thus extracted to the outside. Thereby, of the light C having an incident angle θc of not less than the critical angle with respect to the major surface  10   a  that is a light extraction surface, components that might be lost by total reflection at the major surface  10   a  are extracted to the outside. 
     The light reflection prevention effect increases as the proportion of the area of the first region R 1  in the optical layer  20  increases as viewed in the Z direction, and the light scattering and diffraction effects increase as the proportion of the area of the second region R 2  in the optical layer  20  increases as viewed in the Z direction. In view of the balance between both, the proportion of the area of the second region R 2  is preferably approximately not less than 5% and less than 50%. 
     If the proportion of the area of the second region R 2  is less than 5%, the light scattering effect is too small; and those of approximately 5% or more provide an increased efficiency of extracting light of not less than the critical angle. On the other hand, if the proportion is 50% or more, the region where Fresnel reflection can be reduced is small and the light transmittance T at not more than the critical angle, other than diffraction angles, is reduced. Furthermore, those of 50% or more make it difficult to make a functional separation between the light reflection prevention effect by the first region R 1  and the light scattering and diffraction effects by the second region R 2 . Therefore, the proportion of the area of the second region R 2  is preferably less than 50%. 
     As the dielectric material used for the first particle  22  and the second particle  23 , a material is used that has a relatively large refractive index, in view of the refractive index of the stacked body  10  being approximately not less than 2 and not more than 3.5, and does not cause light absorption by the material at a desired wavelength of light. For example, the first particle  22  and the second particle  23  are made of an oxide or a nitride of at least one selected from the group consisting of titanium, zinc, tin, indium, zirconium, silicon, and tungsten or polystyrene. As the material of the dielectric body  21  in which first particles  22  and second particles  23  are scattered, silicon oxide, an epoxy resin, and a silicone resin are preferable. 
     In the case where, for example, the effect of reducing Fresnel reflection for visible light is obtained using such materials, the thickness t 1  of the first region R 1  including the first particle  22  and the dielectric body  21  is preferably approximately 30 nm or more due to the constraint of the refractive index and the wavelength. 
     Thus, in the semiconductor light emitting element  110  according to the embodiment, by the first region R 1  and the second region R 2  of the optical layer  20 , a light reflection prevention effect and light scattering and diffraction effects are exhibited and the light extraction efficiency is improved. 
       FIG. 6  is a schematic diagram illustrating the configuration of a measurement apparatus of the light extraction efficiency. 
     As shown in  FIG. 6 , a measurement apparatus  200  includes a light source  210 , an integrating sphere  220 , a detection unit  230 , and an output unit  240 . A sample S of which the light extraction efficiency is measured is placed at the integrating sphere  220 . The sample S is irradiated with ultraviolet light (e.g. wavelength: 254 nm) from the light source  210 . The light thereby emitted from the sample S is collected by the integrating sphere  220  and is detected by the detection unit  230 . The output unit  240  outputs the detection result. 
     The light extraction efficiency of the sample S is measured using the measurement apparatus shown in  FIG. 6 . 
     The optical film  20  is fabricated by the following processes. 
     First, a TiO 2  particle paste (PST-400C; manufactured by JGC Catalysts and Chemicals Ltd.) is weighed out to obtain an SOG solution (OCD-T7 T-5500; manufactured by Tokyo Ohka Kogyo Co., Ltd.) with a TiO 2  particle paste content of 3 weight percent, and is sufficiently dispersed by ultrasonic irradiation. Then, the mixture is filtered through a PTFE (polytetrafluoroethylene) filter with a pore size of 5.0 μm to obtain a dispersion solution of TiO 2  particles. 
     Next, the dispersion solution is applied onto a substrate by spin coating at 2000 rpm, and baking treatment at 120° C. for 90 seconds is performed on a hot plate. Then, the SOG solution is cured by heating at 300° C. for 30 minutes under a nitrogen atmosphere; thus, the optical film  20  is completed. 
     The average refractive index of the first region R 1  in the optical film  20  completed is approximately 1.45, the thickness t 1  of the first region R 1  is approximately 400 nm, and the refractive index of the TiO 2  is 2.5. 
     The light extraction efficiency is measured for each of a first sample of only a GaP substrate and a second sample in which the optical film  20  mentioned above is formed on a GaP substrate. 
     Assuming that the light extraction efficiency in the first sample is 1, the light extraction efficiency in the second sample is approximately 2.9. As a reference example, the light extraction efficiency in a third sample having a concave-convex  15  like that shown in  FIG. 2A  is approximately 2.6. 
     When the optical film  20  of the second sample is provided on a red LED with a charge injection electrode formed, the maximum brightness is improved to approximately 2.0 times as compared to the case where the optical film  20  is not provided. 
     Next, optical simulations are described. Herein, simulation results using the RCWA (rigorous coupled wave analysis) method are described as examples. 
     First, it is illustrated that the effective refractive index changes with a medium (corresponding to the first region R 1 ) in which first particles  22  having a sphere-equivalent diameter of 1/10 or less of the wavelength of the light transmitted are scattered in the dielectric body  21 . 
       FIG. 7  is a diagram showing the relationship between the first region and the refractive index. 
       FIG. 7  shows the refractive index n mg  obtained from Maxwell-Garnett and the refractive index n sim  obtained from a simulation calculation in regard to three kinds of first regions R 1 (A), R 1 (B), and R 1 (C). 
     The first region R 1 (A) is a region in which the thickness t 1  is 520 nm, the sphere-equivalent diameter of the first particle  22  is 50 nm, the refractive index of the first particle  22  is 1.8, the refractive index of the dielectric body  21  is 1.4, and the density of first particles  22  is 60 vol %. 
     The first region R 1 (B) is a region in which the thickness t 1  is 275 nm, the sphere-equivalent diameter of the first particle  22  is 25 nm, the refractive index of the first particle  22  is 1.6, the refractive index of the dielectric body  21  is 1.5, and the density of first particles  22  is 40 vol %. 
     The first region R 1 (C) is a region in which the thickness t 1  is 140 nm, the sphere-equivalent diameter of the first particle  22  is 10 nm, the refractive index of the first particle  22  is 2.5, the refractive index of the dielectric body  21  is 1.6, and the density of first particles  22  is 20 vol %. 
     In the first region R 1 (A), the refractive index n mg  obtained from Maxwell-Garnett is 1.68, and the refractive index n sim  obtained from the simulation calculation is 1.68. 
     In the first region R 1 (B), the refractive index n mg  obtained from Maxwell-Garnett is 1.54, and the refractive index n sim  obtained from the simulation calculation is 1.55. 
     In the first region R 1 (C), the refractive index n mg  obtained from Maxwell-Garnett is 1.76, and the refractive index n sim  obtained from the simulation calculation is 1.78. 
     As illustrated above, it is found that the refractive index n sim  obtained from the simulation calculation almost agrees with the refractive index n mg  obtained from Maxwell-Garnett. 
     In the first region R 1 , adjustment is made using the size and refractive index of the first particle  22  and the refractive index and film thickness of the dielectric body  21  to obtain an arbitrary refractive index. 
       FIG. 8  is a diagram illustrating simulation results showing the relationship between the wavelength and the light transmittance. 
       FIG. 8  shows simulation calculation results (spectrum distribution) of the relationship between the wavelength λ (μm) and the light transmittance T for an optical film similar to the first region R 1 (A) shown in  FIG. 7 . 
     As shown in  FIG. 8 , the optical film similar to the first region R 1 (A) exhibits the characteristic that the light transmittance T becomes high at specific wavelengths A. That is, it is found that a high reflection prevention effect is obtained at the wavelengths A at which the light transmittance T becomes high. 
     The spectrum distribution shown in  FIG. 8  changes with the average refractive index of the first region R 1  formed on a substrate in which first particles  22  having a sphere-equivalent diameter of 1/10 or less of the wavelength of the light transmitted are scattered. Therefore, the average refractive index of the first region R 1  can be calculated from the spectrum distribution. 
     Next, simulation results of scattering in the second region R 2  are described. 
       FIG. 9  to  FIG. 11  are diagrams illustrating simulation results of the direction of scattering due to the second particle. 
     In the drawings, FS indicates the direction of forward scattering, and BS indicates the direction of backward scattering. The scattering is relative values on the assumption that the maximum value is 1. 
       FIG. 9  shows scattering in the case where the sphere-equivalent diameter of the second particle  23  is 200 nm, the refractive index of the second particle  23  is 1.5, the refractive index of the dielectric body  21  is 1.0, and the wavelength is 400 nm. 
       FIG. 10  shows scattering in the case where the sphere-equivalent diameter of the second particle  23  is 300 nm and the other conditions are the same as  FIG. 9 . 
       FIG. 11  shows scattering in the case where the sphere-equivalent diameter of the second particle  23  is 1000 nm and the other conditions are the same as  FIG. 9 . 
     From the simulation results mentioned above, forward scattering is stronger in the case shown in  FIG. 10  where the sphere-equivalent diameter of the second particle  23  is 300 nm than in the case shown in  FIG. 9  where the sphere-equivalent diameter of the second particle  23  is 200 nm. On the other hand, when the sphere-equivalent diameter of the second particle  23  is 1000 nm as shown in  FIG. 11 , the direction dependence of scattering is strong as compared to the case shown in  FIG. 10  where the sphere-equivalent diameter of the second particle  23  is 300 nm. 
     Thus, the sphere-equivalent diameter of the second particle  23  is preferably more than 300 nm and less than 1000 nm. 
       FIG. 12  to  FIG. 14  are diagrams showing simulation calculation results of the light transmittance versus the incident angle θc. 
     In this simulation calculation, the center-of-mass distance between second particles  23 , the film thickness of the dielectric body  21 , and the area ratio (the proportion to the area of the major surface  10   a ) of second particles  23  are changed in the case where the sphere-equivalent diameter of the second particle  23  is 400 nm, the refractive index of the second particle  23  is 2.5, and the refractive index of the dielectric body  21  is 1.4. 
       FIG. 12  shows simulation results in the case where the center-of-mass distance between second particles  23  is 1600 nm, the film thickness of the dielectric body  21  is 30 nm, and the area ratio of second particles  23  is 5%. 
       FIG. 13  shows simulation results in the case where the center-of-mass distance between second particles  23  is 650 nm, the film thickness of the dielectric body  21  is 400 nm, and the area ratio of second particles  23  is 40%. 
       FIG. 14  shows simulation results in the case where the center-of-mass distance between second particles  23  is 500 nm, the film thickness of the dielectric body  21  is 30 nm, and the area ratio of second particles  23  is 80%. 
     As shown in  FIG. 12 , the simulation results mentioned above show that light of not less than the critical angle is totally reflected in the case where the center-of-mass distance between second particles  23  is as wide as 1600 nm and the area ratio is as low as 5%. As shown in  FIG. 13 , when the center-of-mass distance between second particles  23  is 650 nm and the area ratio is 40%, the light transmittance T of not less than the critical angle is increased without causing a large decrease in the light transmittance T of not more than the critical angle. As shown in  FIG. 14 , when the center-of-mass distance between second particles  23  is as narrow as 500 nm and the area ratio is as high as 80%, the light transmittance T of not more than the critical angle is greatly decreased. 
     According to the simulation, the area ratio of second particles  23  is preferably approximately not less than 5% and not more than 50%. Thereby, in the semiconductor light emitting element  110  according to the embodiment, the light transmittance T is improved in a wide range of incident angles θc, and an improvement in the light extraction efficiency is achieved. 
     In the semiconductor light emitting element  110  according to the embodiment, the optical layer  20  that provides high light transmissivity for a wide range of incident angles θc is provided on the major surface  10   a  of the stacked body  10 ; thereby, the brightness properties of the semiconductor light emitting element  110  are improved. 
     As described above, the semiconductor light emitting element  110  according to the embodiment can improve the light extraction efficiency. 
     Hereinabove, embodiments and modification examples thereof are described. However, the invention is not limited to these examples. For example, one skilled in the art may appropriately make additions, removals, and design modifications of components to the embodiments or the modification examples thereof described above, and may appropriately combine features of the embodiments; such modifications also are included in the scope of the invention to the extent that the spirit of the invention is included. 
     For example, although the embodiments and the modification examples described above use the case where the first conductivity type is the n-type and the second conductivity type is the p-type, the invention can be practiced also by setting the first conductivity type to the p-type and the second conductivity type to the n-type. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the invention.