Abstract:
An organic light-emitting display apparatus includes a pixel electrode, a light emission layer over the pixel electrode, an opposite electrode covering the light emission layer, a plurality of upper layers over the opposite electrode, a light-shielding layer over the upper layers. A distance L between an edge of an emission area of the light emission layer and an edge of the light-shielding layer when viewed in a thickness direction satisfies Inequality below: 
     
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   Inequality 
                   ] 
                 
               
             
           
         
       
       
         
           
             wherein m represents the number of the upper layers, n i  and d i  represent a refraction index and a thickness of each of the upper layers, respectively, d BM  represents a thickness of the light-shielding layer, n CF  represents a refraction index of the color filter layer, n  air  represents a refraction index of air, and θ air  represents a refraction angle in external air after light generated from the light emission layer passes through the color filter layer.

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
       [0001]    This application is a divisional of U.S. patent application Ser. No. 15/147,758, filed May 5, 2016, which claims priority under 35 U.S.C, §119 of Korean Patent Application No. 10-2015-0138613, filed on Oct. 1, 2015, in the Korean Intellectual Property Office, the disclosures of which are incorporated by reference herein in their entireties. 
     
    
     BACKGROUND 
     1. Field 
       [0002]    One or more embodiments relate to an organic light-emitting display apparatus, and more particularly, to an organic light-emitting display apparatus with improved extraction efficiency of light. 
       2. Discussion of the Related Technology 
       [0003]    In a general top-emission type organic light-emitting display apparatus, light emitted from an emission layer passes through a cathode, layers above the cathode, and is emitted externally. As the light emitted from the light emission layer passes through various layers, refraction of light may occur at interfaces and an optical path is determined accordingly, 
       SUMMARY 
       [0004]    However, from among light emitted from an emission layer of a typical organic light-emitting display apparatus, a large proportion of light is not externally emitted. This leads to brightness reduction, and thus increases power consumption to increase brightness. 
         [0005]    Thus, one or more embodiments are directed to an organic light-emitting display apparatus with improved extraction efficiency of light. 
         [0006]    Additional aspects will be set forth in part in the description which follows and, in part, will be apparent from the description, or may be learned by practice of the presented embodiments. 
         [0007]    One aspect of the invention provides an organic light-emitting display apparatus, which may comprise: a pixel electrode disposed over a substrate; a light emission layer disposed over the pixel electrode; an opposite electrode covering the light emission layer; a plurality of upper layers disposed over the opposite electrode, wherein the number of the plurality of upper layers is m which represents a natural number greater than one; a light-shielding layer disposed over the plurality of upper layers, the light-shielding layer not overlapping the light emission layer; and a color filter layer disposed over the upper layers, wherein L is defined by a distance between an edge of an emission area of the light emission layer and an edge of the light-shielding layer when viewed in a viewing direction perpendicular to a major surface of the substrate, wherein the distance L satisfies Inequality below: 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   Inequality 
                   ] 
                 
               
             
           
         
       
     
         [0000]    wherein n i  represents a refraction index of each of the upper layers, d i  represents a thickness of each of the upper layers, d BM  represents a thickness of the light-shielding layer, n CF  represents a refraction index of the color filter layer, n air  represents a refraction index of air, and θ air  represents a refraction angle in external air after light generated from the light emission layer passes through the color filter layer. 
         [0008]    In the foregoing apparatus, the display apparatus may further comprise a pixel-defining layer covering a boundary of the pixel electrode such that a central area of the pixel electrode is exposed through a hole defined by the pixel-defining layer. The emission area of the light emission layer may correspond to an area of the pixel electrode, which is not covered by the pixel-defining layer. The edge of the emission area of the light emission layer may correspond to a boundary of the area of the pixel electrode, which is not covered by the pixel-defining layer. The display apparatus may further comprise a pixel-defining layer disposed over the substrate and defining a hole that allows a portion of the light emission layer not to overlap the pixel-defining layer when viewed in the viewing direction, wherein the emission area is defined by the non-overlapping portion of the light emission layer. 
         [0009]    Still in the foregoing apparatus, a lowermost layer among the plurality of upper layers may directly contact the opposite electrode. A bottom surface of the color filter layer facing the light emission layer and a bottom surface of the light-shielding layer facing the light emission layer may be on the same plane. A thickness of the color filter layer may be substantially equal to or substantially greater than a thickness of the light-shielding layer. θ air  may be 90°. The plurality of upper layers may comprise a first inorganic encapsulating layer, an organic encapsulating layer on the first inorganic encapsulating layer, and a second inorganic encapsulating layer on the organic encapsulating layer. Each of the first inorganic encapsulating layer and the second inorganic encapsulating layer may comprise at least one selected from silicon oxide, silicon nitride, and silicon oxynitride, and the organic encapsulating layer may comprise at least one selected from polyacrylate, polyethylene terephthalate, polyethylene naphthalate, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate. The organic encapsulating layer may be disposed between and directly contact both the first and second inorganic encapsulating layers. 
         [0010]    Yet in the foregoing apparatus, the plurality of upper layers may comprise a plurality of inorganic encapsulating layers and a plurality of organic encapsulating layers which are alternatively stacked on one another. Each of the inorganic encapsulating layers may comprise at least one selected from silicon oxide, silicon nitride, and silicon oxynitride, and each of the organic encapsulating layers may comprise at least one selected from polyacrylate, polyethylene terephthalate, polyethylene naphthalate, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate. 
         [0011]    The edge of the light-shielding layer may define an opening through which light emitted from the light emission layer toward the upper layers travels, wherein the edge of the light-shielding layer forms a closed loop surrounding the emission area of the light emission layer when viewed in the viewing direction. The edge of the light-shielding layer may define an opening, wherein the distance L is defined to satisfy said Inequality such that substantially the entire portion of light emitted from the light emission layer toward the upper layers travels through the opening. The edge of the light-shielding layer may face the edge of the emission area of the light emission layer when viewed in the viewing direction, 
         [0012]    Another aspect of the invention provides an organic light-emitting display apparatus, which may comprise: an array of pixels disposed over a substrate, each pixel comprising a first sub-pixel comprising a first light emission layer configured to emit first light having a first wavelength within a first wavelength range, a second sub-pixel comprising a second light emission layer configured to emit second light having a second wavelength within a second wavelength range, the second wavelength of the second light being longer than a wavelength of light within the first wavelength range, and a third sub-pixel comprising a third light emission layer configured to emit third light having a third wavelength within a third wavelength range, the third wavelength of the third light being longer than a wavelength of light within the second wavelength range; an encapsulating layer disposed over the first to third sub-pixels; a light-shielding layer disposed over the encapsulating layer; and a color filter layer disposed on the encapsulating layer, wherein L 1 &lt;L 2 &lt;L 3  is satisfied when L 1  represents a distance between an edge of an emission area of the first light emission layer and a first edge of the light-shielding layer when viewed in a viewing direction perpendicular to a major surface of the substrate, L 2  represents a distance between an edge of an emission area of the second light emission layer and a second edge of the light-shielding layer when viewed in the viewing direction, and L 3  represents a distance between an edge of an emission area of the third light emission layer and a third edge of the light-shielding layer when viewed in the viewing direction. 
         [0013]    In the foregoing apparatus, the first edge of the light-shielding layer may define an opening through which light emitted from the first light emission layer travels, wherein the distance L 1  is determined such that substantially the entire amount of the light emitted from the first light emission layer toward the encapsulation layer travels through the opening. The first edge may form a first closed loop surrounding the emission area of the first light emission layer, wherein the second edge may form a second closed loop surrounding the emission area of the second light emission layer, wherein the third edge may form a third closed loop surrounding the emission area of the third light emission layer. 
         [0014]    According to one or more embodiments, an organic light-emitting display apparatus includes a pixel electrode, an emission layer over the pixel electrode, an opposite electrode covering the emission layer, m number of upper layers over the opposite electrode, a light-shielding layer over the upper layers, the light-shielding layer not overlapping the emission layer, and a color filter layer over the upper layers. A distance L between an edge of an emission area of the emission layer toward the light-shielding layer and an edge of the light-shielding layer toward the emission layer satisfies Inequality below: 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   Inequality 
                   ] 
                 
               
             
           
         
       
     
         [0015]    wherein n i  represents a refraction index of each of the upper layers, d i  represents a thickness of each of the upper layers, d BM  represents a thickness of the light-shielding layer, n CF  represents a refraction index of the color filter layer, n air  represents a refraction index of air, and θ air  represents a refraction angle in external air after light generated from the emission layer passes through the color filter layer. 
         [0016]    The organic light-emitting display apparatus may further include a pixel-defining layer covering a boundary of the pixel electrode such that a central area of the pixel electrode is exposed, and the upper layers may correspond to the pixel electrode and the pixel-defining layer. 
         [0017]    The emission area of the emission layer may correspond to an area of the pixel electrode, which is not covered by the pixel-defining layer. The edge of the emission area of the emission layer toward the light-shielding layer may correspond to a boundary of the area of the pixel electrode, which is not covered by the pixel-defining layer. 
         [0018]    A lowermost layer toward the emission layer, from among the m number of upper layers, may directly contact the opposite electrode. 
         [0019]    A bottom surface of the color filter layer toward the emission layer and a bottom surface of the light-shielding layer toward the emission layer may be on a same plane. A thickness of the color filter layer may be equal to or greater than a thickness of the light-shielding layer. 
         [0020]    θ air  may be 90°. 
         [0021]    The m number of upper layers may include a first inorganic encapsulating layer, an organic encapsulating layer on the first inorganic encapsulating layer, and a second inorganic encapsulating layer on the organic encapsulating layer. Each of the first inorganic encapsulating layer and the second inorganic encapsulating layer may include at least one selected from silicon oxide, silicon nitride, and silicon oxynitride. The organic encapsulating layer may include at least one selected from polyacrylate, polyethylene terephthalate, polyethylene naphthalate, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate. 
         [0022]    The m number of upper layers may include a plurality of inorganic encapsulating layers and a plurality of organic encapsulating layers which are alternatively stacked on one another. Each of the inorganic encapsulating layers may include at least one selected from silicon oxide, silicon nitride, and silicon oxynitride. Each of the organic encapsulating layers may include at least one selected from polyacrylate, polyethylene terephthalate, polyethylene naphthalate, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate, 
         [0023]    According to one or more embodiments, an organic light-emitting display apparatus includes a first sub-pixel comprising a first emission layer emitting first light having wavelength belonging to a first wavelength band, a second sub-pixel comprising a second emission layer emitting second light having wavelength belonging to a second wavelength band, the wavelength of the second light being longer than wavelength of light belong to the first wavelength band, a third sub-pixel comprising a third emission layer emitting third light having wavelength belonging to a third wavelength band, the wavelength of the third light being longer than wavelength of light belonging to the second wavelength band, an encapsulating layer over the first to third sub-pixels, a light-shielding layer over the encapsulating layer and corresponding to areas between the first to third sub-pixels, and a color filter layer on the encapsulating layer. L 1 &lt;L 2 &lt;L 3  is satisfied when L 1  represents a distance between an edge of an emission area of the first emission layer toward the light-shielding layer and an edge of the light-shielding layer toward the first emission layer, L 2  represents a distance between an edge of an emission area of the second emission layer toward the light-shielding layer and an edge of the light-shielding layer toward the second emission layer, and L 3  represents a distance between an edge of an emission area of the third emission layer toward the light-shielding layer and an edge of the light-shielding layer toward the third emission layer. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0024]    These and/or other aspects will become apparent and more readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings in which: 
           [0025]      FIG. 1  is a cross-sectional view schematically illustrating a portion of an organic light-emitting display apparatus according to an embodiment; 
           [0026]      FIG. 2  is a conceptual view schematically illustrating an optical path in the portion of the organic light-emitting display apparatus of  FIG. 1 ; 
           [0027]      FIG. 3  is a graph of a refraction index according to wavelengths of silicon oxide; 
           [0028]      FIG. 4  is a graph of a refraction index according to wavelengths of silicon nitride; 
           [0029]      FIG. 5  is a graph of a refraction index according to wavelengths of polyacrylate; and 
           [0030]      FIG. 6  is a graph of a refraction index according to wavelengths of polyethylene terephthalate. 
       
    
    
     DETAILED DESCRIPTION 
       [0031]    As the inventive concept allows for various changes and numerous embodiments, particular embodiments will be illustrated in the drawings and described in the written description. The effect and features of the inventive concept and the method of realizing the effect and the features will be clear with reference to the embodiments described below with reference to the drawings. However, the inventive concept may be embodied in various forms and should not be construed as being limited to the embodiments. As used herein, the term “and/or” includes any and all combinations of one or more of the associated listed items. Expressions such as “at least one of,” when preceding a list of elements, modify the entire list of elements and do not modify the individual elements of the list. 
         [0032]    Hereinafter, the embodiments will be described with reference to the drawings. Like reference numerals refer to like elements in the drawings, and thus, descriptions of similar or identical elements will not be repeated. 
         [0033]    It will be understood that when a layer, region, or component is referred to as being formed or disposed “on,” another layer, region, or component, it can be formed or disposed directly on and contact the other layer, region, or component, or it can be formed or disposed indirectly on the other layer, region or component such that one or more intervening layers, regions or components may be present therebetween. 
         [0034]    Sizes of elements in the drawings may be exaggerated for convenience of explanation. In other words, since sizes and thicknesses of components in the drawings are arbitrarily illustrated for convenience of explanation, the following embodiments are not limited thereto. 
         [0035]    In the following examples, the x-axis, the y-axis and the z-axis are not limited to three axes of a rectangular coordinate system, and may be interpreted in a broader sense. For example, the x-axis, the y-axis, and the z-axis may be perpendicular to one another, or may represent different directions that are not perpendicular to one another. 
         [0036]      FIG. 1  is a cross-sectional view schematically illustrating a portion of an organic light-emitting display apparatus according to an embodiment; 
         [0037]    The organic light-emitting display apparatus according to the present embodiment includes a pixel electrode  210 , an emission layer  220  over the pixel electrode  210 , four upper layers, namely, an opposite electrode  230 , a first inorganic encapsulating layer  310 , an organic encapsulating layer  320 , and a second inorganic encapsulating layer  330  over the light emission layer  220 , a light-shielding layer  410  over the upper layers  230 ,  310 ,  320 , and  330 , and a color filter layer  420  over the upper layers  230 ,  310 ,  320 , and  330 . 
         [0038]    When necessary, as shown in  FIG. 1 , a thin film transistor TFT or a capacitor Cap may be provided on a substrate  100 , and the pixel electrode  210  may be electrically connected to the thin film transistor TFT. The substrate  100  may include various materials, for example, a glass material, a metallic material, or a plastic material such as polyethylene terephthalate (PET), polyethylene naphthalate (PEN), and polyimide. Also, a buffer layer  110 , a gate insulating layer  130 , an interlayer insulating layer  150 , and a planarization layer  170  may be provided on the substrate  100 . The buffer layer  110  may prevent impurities from penetrating into a semiconductor layer of the thin film transistor TFT. The gate insulating layer  130  may insulate the semiconductor layer of the thin film transistor TFT from a gate electrode. The interlayer insulating layer  150  may insulate a source/drain electrode and the gate electrode of the thin film transistor TFT from each other. The planarization layer  170  may cover the thin film transistor TFT and have a substantially flat top surface. 
         [0039]    The pixel electrode  210  may be a (semi) transparent electrode or a reflection electrode. When the pixel electrode  210  is a (semi) transparent electrode, the pixel electrode  210  may include, for example, indium tin oxide (ITO), indium zinc oxide (IZO), zinc oxide ZnO), indium oxide (In 2 O 3 ), indium gallium oxide (IGO), or aluminum zinc oxide (AZO). When the pixel electrode  210  is a reflection electrode, the pixel electrode  210  may include a reflection layer including silver (Ag), magnesium (Mg), aluminum (Al), platinum (Pt), palladium (Pd), gold (Au), nickel (Ni), neodymium (Nd), iridium (Ir), chrome (Cr), or a compound thereof, and a layer including ITO, IZO, ZnO, or ln 2 O 3 . However, composition and materials of the pixel electrode  210  are not limited to the above and various modifications may be adapted. 
         [0040]    In order to define a location of the light emission layer  220  among layers above the pixel electrode  210 , a pixel-defining layer  180  may be provided as shown in  FIG. 1 . The pixel-defining layer  180  may cover a boundary of the pixel electrode  210  such that a central area of the pixel electrode  210  is exposed. Accordingly, the pixel-defining layer  180  may define a pixel. Also, the pixel-defining layer  180  may increase a distance between an edge of the pixel electrode  210  and the opposite electrode  230  above the pixel electrode  210  so as to prevent an arc at the edge of the pixel electrode  210 . 
         [0041]    The light emission layer  220  is located on the pixel electrode  210 . An intermediate layer may be provided between the pixel electrode  210  and the light emission layer  220 . For example, a hole injection layer and/or a hole transport layer may be provided on the pixel electrode  210 , and the light emission layer  220  may be provided on the hole injection layer and/or the hole transport layer. 
         [0042]    As shown in  FIG. 1 , the opposite electrode  230  is located on the light emission layer  220 . The opposite electrode  230  may be integrally formed as one body so that one opposite electrode  230  may correspond to a plurality of pixels. Therefore, the opposite electrode  230  may correspond to not only the light emission layer  220  but also top surfaces of the pixel-defining layer  180 . The opposite electrode  230  may be a (semi) transparent electrode. Accordingly, the opposite electrode  230  may include a layer including lithium (Li), calcium (Ca), LiF/Ca, LiF/Al, Al, Mg, or a compound thereof, and a layer including a (semi) transparent material such as ITO, IZO, ZnO, or In 2 O 3 . 
         [0043]    The pixel electrode  210 , the light emission layer  220 , and the opposite electrode  230  may be regarded as an organic light-emitting device (OLED)  200 . The OLED  200  may emit light having brightness that is determined according to an electric signal applied to the pixel electrode  210  via the thin film transistor TFT. 
         [0044]    An encapsulation layer  300  is provided on the OLED  200 . The encapsulation layer  300  may not only correspond to the light emission layer  220  but also the top surfaces of the pixel-defining layer  180 . The encapsulation layer  300  may have a multi-layer structure. For example, the encapsulation layer  300  may include the first inorganic encapsulating layer  310 , the organic encapsulating layer  320 , and the second inorganic encapsulating layer  330 , as shown in  FIG. 1 . The encapsulation layer  300  may protect the OLED  200  from external impurities such as oxygen or moisture, 
         [0045]    The first inorganic encapsulating layer  310  or the second inorganic encapsulating layer  330  may include various materials, for example, silicon nitride, silicon oxide, and/or silicon oxynitride, or metal oxide, metal nitride, metal oxynitride, or metal carbide. The organic encapsulating layer  320  between the first and second inorganic encapsulating layers  310  and  330  may planarize curves of the first inorganic encapsulating layer  310 . Also, since organic encapsulating layer  320  covers the first inorganic encapsulating layer  310 , even when there is a crack in the first inorganic encapsulating layer  310 , the crack may not extend further into the second inorganic encapsulating layer  330 . The organic encapsulating layer  320  may include at least one selected from the group consisting of polyacrylate, PET, PEN, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate. 
         [0046]    The light-shielding layer  410  and the color filter layer  420  are provided on the encapsulation layer  300 . The light-shielding layer  410  is provided on the encapsulation layer  300  without overlapping the light emission layer  220 , and the color filter layer  420  is provided on the encapsulation layer  300  and overlaps the light emission layer  220 . Since the light-shielding layer  410  does not overlap the light emission layer  220 , the light-shielding layer  410  may be regarded as being located correspondingly to areas between pixels. For example, when viewing the organic light-emitting display apparatus on z-axis that is perpendicular to an xy-plane and extends in a direction of perpendicular to a major surface of the substrate  100  or a thickness direction of the display apparatus, the light-shielding layer  410  may surround each of the pixels. The light-shielding layer  410  may be regarded as surrounding an emission area of the light emission layer  220 . 
         [0047]    The light-shielding layer  410  may prevent external light reflection and increase contrast of the organic light-emitting display apparatus. The light-shielding layer  410  may include a material such as Cr, Al, silicon (Si), or an oxide thereof. The color filter layer  420  may restrict a wavelength of light to be emitted externally, from among light generated by the light emission layer  220 , within a predetermined wavelength band, or may prevent a portion of external light, which is incident on the color filter layer  420  and does not belong to the predetermined wavelength band, from being reflected externally. 
         [0048]    Since the light-shielding layer  410  and the color filter layer  420  are located on the encapsulation layer  300 , a bottom surface of the light-shielding layer  410  facing the light emission layer  220  (−z direction) and a bottom surface of the color filter layer  420  facing the light emission layer  220  (−z direction) may be on the same plane. In this case, the color filter layer  420  may be thicker than the light-shielding layer  410 , as shown in  FIG. 1 , and thus, the color filter layer  420  may cover the an upper surface of the light-shielding layer  410 . However, the embodiments are not limited thereto, and the color filter layer  420  may be as thick as the light-shielding layer  410 . 
         [0049]    The organic light-emitting display apparatus according to the present embodiment may further include a window  500 . The window  500  is a transparent layer and be located at an outermost area of the organic light-emitting display apparatus. 
         [0050]    Hereinafter, an optical path in the organic light-emitting display apparatus according to the present embodiment will be described. 
         [0051]      FIG. 2  is a conceptual view schematically illustrating an optical path in the portion of the organic light-emitting display apparatus of  FIG. 1 .  FIG. 2  shows a sectional view taken along a plane which is perpendicular to a major surface of a substrate of the display apparatus. Although  FIG. 2  shows that the organic light-emitting display apparatus according to the present embodiment does not satisfy the condition of Inequality 9 shown below, this is only for convenience of description and illustration. As shown in  FIG. 2 , light emitted by the light emission layer  220  passes through the opposite electrode  230 , the encapsulation layer  300 , the color filter layer  420 , and the window  500  and is emitted externally. In this case, refraction occurs at interfaces based on Snell&#39;s law. 
         [0052]    In this case, the opposite electrode  230  may have a thickness of only few nm (nanometer) to tens of nm, whereas the encapsulation layer  300  and the light-shielding layer  410  may be much thicker than the opposite electrode  230 , e.g., about few μm. An electron transport layer and/or an electron injection layer may be provided between the light emission layer  220  and the opposite electrode  230 . However, the light emission layer  220 , the electron transport layer, and the electron injection layer may have a thickness of only few nm to tens of nm. 
         [0053]    Hereinafter, with regard to an optical path, by which light generated by the light emission layer  220  travels before being externally emitted, a displacement in a direction (+x direction) perpendicular to a forward direction (+z direction) that is perpendicular to the pixel electrode  210  will be described. Since the light emission layer  220 , the electron transport layer, and the electron injection layer have a thickness of only few nm to tens of nm, when describing the displacement in the direction (+x direction) in which light generated by the light emission layer  220  travels until being externally emitted, it is acceptable to only consider a displacement in the encapsulation layer  300  and disregard a displacement in the electron transport layer and/or the electron injection layer, or the opposite electrode  230 . 
         [0054]    A refraction index of the first inorganic encapsulating layer  310  may be indicated by ‘n 1 ,’ a refraction index of the organic encapsulating layer  320  may be indicated by ‘n 2 ,’ a refraction index of the second inorganic encapsulating layer  330  may be indicated by ‘n 3 ,’ a refraction index of the color filter layer  420  may be indicated by ‘n CF ,’ a refraction index of the window  500  may be indicated by ‘n w .’ Light incident angle at an interface between the first inorganic encapsulating layer  310  and the organic encapsulating layer  320  is indicated by ‘θ 1 ,’ a light refraction angle at the interface is indicated by ‘θ 2 ,’ a light refraction angle at an interface between the organic encapsulating layer  320  and the second inorganic encapsulating layer  330  is indicated by ‘θ 3 ,’ a light refraction angle at an interface between the second inorganic encapsulating layer  330  and the color filter layer  420  is indicated by ‘θ CF ,’ a light refraction angle at an interface between the color filter layer  420  and the window  500  is indicated by ‘θ w ,’ and a light refraction angle at an interface between the window  500  and external air is indicated by ‘θ air .’ The relationship between the indices and angles at the interfaces may be as defined below in Equation 1 based on Snell&#39;s law (wherein i is 1 or 2). 
         [0000]        n   i  sin θ i   =n   i+1  sin θ i+1   , n   3  sin θ 3   =n   CF  sin θ CF  
 
         [0000]        n   CF sin θ CF   =n   w  sin θ w   , n   w  sin θ w   =n   air  sine θ air    [Equation 1]
 
         [0055]    Equation 2 may be derived based on a relation of the interface between the window  500  and external air in Equation 1. 
         [0000]    
       
         
           
             
               
                 
                   
                     n 
                     w 
                   
                   = 
                   
                     
                       n 
                       air 
                     
                      
                     
                       
                         sin 
                          
                         
                             
                         
                          
                         
                           θ 
                           air 
                         
                       
                       
                         sin 
                          
                         
                             
                         
                          
                         
                           θ 
                           w 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
           
         
       
     
         [0056]    Also, Equation 3 may be derived based on the relation of the interface between the color filter layer  420  and the window  500  in Equation 1 and Equation 2. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       n 
                       CF 
                     
                     = 
                     
                       
                         
                           n 
                           w 
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               w 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               CF 
                             
                           
                         
                       
                       = 
                       
                         
                           n 
                           air 
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               air 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               CF 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       θ 
                       CF 
                     
                     = 
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               n 
                               air 
                             
                             
                               n 
                               CF 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           
                             θ 
                             air 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
           
         
       
     
         [0057]    Likewise, Equation 4 may be derived based on the relation of the interface between the second inorganic encapsulating layer  330  and the color filter layer  420  in Equation 1 and Equation 3. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       n 
                       3 
                     
                     = 
                     
                       
                         
                           n 
                           CF 
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               CF 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               3 
                             
                           
                         
                       
                       = 
                       
                         
                           n 
                           air 
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               air 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               3 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       θ 
                       4 
                     
                     = 
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               n 
                               air 
                             
                             
                               n 
                               4 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           
                             θ 
                             air 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
         [0058]    Also, Equation 5 may be derived based on the relation of the interface between the first inorganic encapsulating layer  310  and the organic encapsulating layer  320  and the relation of the interface between the organic encapsulating layer  320  and the second inorganic encapsulating layer  330  in Equation 1 and Equation 4 (wherein i is 1 or 2). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       n 
                       i 
                     
                     = 
                     
                       
                         
                           n 
                           
                             i 
                             + 
                             1 
                           
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               
                                 i 
                                 + 
                                 1 
                               
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               i 
                             
                           
                         
                       
                       = 
                       
                         
                           n 
                           air 
                         
                          
                         
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               air 
                             
                           
                           
                             sin 
                              
                             
                                 
                             
                              
                             
                               θ 
                               i 
                             
                           
                         
                       
                     
                   
                   , 
                   
                     
 
                   
                    
                   
                     
                       θ 
                       i 
                     
                     = 
                     
                       
                         sin 
                         
                           - 
                           1 
                         
                       
                        
                       
                         ( 
                         
                           
                             
                               n 
                               air 
                             
                             
                               n 
                               i 
                             
                           
                            
                           sin 
                            
                           
                               
                           
                            
                           
                             θ 
                             air 
                           
                         
                         ) 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
           
         
       
     
         [0059]    A distance traveled by light in the first inorganic encapsulating layer  310  in a direction (+x direction) perpendicular to a direction (+z direction) perpendicular to the pixel electrode  210  is indicated by Δx 1 ; a distance traveled by light in the organic encapsulating layer  320  in the direction (+x direction) perpendicular to the forward direction (+z direction) is indicated by Δx 2 ; a distance traveled by light in the second inorganic encapsulating layer  330  in the direction (+x direction) perpendicular to the forward direction (+z direction) is indicated by Δx 3 ; and a distance traveled by light in the forward direction (+z direction) in the color filter layer  420  by a thickness of the light-shielding layer  410  in the direction (+x direction) perpendicular to the forward direction (+z direction) is indicated by Δx BM . Then, a total distance Δx traveled by light in a direction perpendicular to the forward direction (+z direction) is as defined below in Equation 6. 
         [0000]    
       
         
           
             
               
                 
                   
                     Δ 
                      
                     
                         
                     
                      
                     x 
                   
                   = 
                   
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           3 
                         
                          
                         
                           Δ 
                            
                           
                               
                           
                            
                           
                             x 
                             i 
                           
                         
                       
                       + 
                       
                         Δ 
                          
                         
                             
                         
                          
                         
                           x 
                           BM 
                         
                       
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           3 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                               
                           
                            
                           
                             θ 
                             i 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         tan 
                          
                         
                             
                         
                          
                         
                           θ 
                           CF 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
           
         
       
     
         [0060]    Equation 7 is derived by substituting Equations 3 to 5 into Equation 6. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       x 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           3 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
           
         
       
     
         [0061]    Heretofore, an example in which three layers are provided between the opposite electrode  230  and the color filter layer  420  has been described. In embodiments, a plurality of upper layers may be provided on the opposite electrode  230  and the color filter layer  420  may be above the upper layers. In this case, Equation 7 may be modified as below in Equation 8 (wherein the number of the plurality of upper layers is represented by m which is a natural number of at least 1). 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       Δ 
                        
                       
                           
                       
                        
                       x 
                     
                     = 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
         [0062]    In this case, suppose that ‘L’ represents a distance between an edge of the emission area of the light emission layer  220  in the direction (+x direction) which faces the light-shielding layer  410  and an edge of the light-shielding layer  410  in a direction (−x direction) which faces the light emission layer  220 . Then, the organic light-emitting display apparatus according to the present embodiment satisfies the following Inequality 9. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       i 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     
                                       n 
                                       air 
                                     
                                     
                                       n 
                                       CF 
                                     
                                   
                                    
                                   sin 
                                    
                                   
                                       
                                   
                                    
                                   
                                     θ 
                                     air 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Inequality 
                      
                     
                         
                     
                      
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
         [0063]    When L does not satisfy Inequality 9, this indicates that at least some of the light generated at the edge of the emission area of the light emission layer  220  in the direction (+x direction) toward the light-shielding layer  410  is blocked by the light-shielding layer  410  and not emitted externally, thereby decreasing light efficiency. 
         [0064]    However, L may satisfy Inequality 9 in the organic light-emitting display apparatus according to the present embodiment, and thus, extraction efficiency of light generated by the emission area of the light emission layer  220  may substantially increase. In this case, the emission area of the light emission layer  220  may correspond to an area of the pixel electrode  210 , which is not covered by the pixel-defining layer  180 . Also, the edge of the emission area of the light emission layer  220  in the direction (+x direction) toward the light-shielding layer  410  may be regarded as a portion of the light emission layer  220 , which corresponds to a boundary of the area of the pixel electrode  210 , which is not covered by the pixel-defining layer  180 . 
         [0065]    According to the above description, the encapsulation layer  300  includes three layers, i.e., the first inorganic encapsulating layer  310 , the organic encapsulating layer  320 , and the second inorganic encapsulating layer  330 . In embodiments, the plurality of upper layers include the first inorganic encapsulating layer  310 , the organic encapsulating layer  320  on the first inorganic encapsulating layer  310 , and the second inorganic encapsulating layer  330  on the organic encapsulating layer  320 . However, the embodiments are not limited thereto. For example, the plurality of upper layers may include a plurality of inorganic encapsulating layers and a plurality of organic encapsulating layers which are alternatively stacked on one another. Each of the inorganic encapsulating layers may include at least one selected from silicon oxide, silicon nitride, and silicon oxynitride, and each of the organic encapsulating layers may include at least one selected from polyacrylate, PET, PEN, polycarbonate, polyimide, polyethylene sulfonate, polyoxymethylene, and polyarylate. 
         [0066]    From among the plurality of upper layers described in relation to Inequality 9, the lowermost layer in the direction (−z direction) facing the light emission layer  220  may directly contact the opposite electrode  230 . In embodiments, other layers such as a capping layer or a film layer may be provided between the opposite electrode  230  and the encapsulation layer  300 . In this case, the plurality of upper layers may be regarded as including the encapsulation layer  300  and other layers, e.g., a capping layer or a film layer. Also, when other layers are between the encapsulation layer  300  and the color filter layer  420 , the other layers are also included in the plurality of upper layers described above in relation to Inequality 9. 
         [0067]    With regard to Inequality 9, ‘L’ is a function of respective thicknesses and refraction indices of the plurality of upper layers, a thickness of the light-shielding layer  410 , a refraction index of the color filter layer  420 , a refraction index of air, and a final refraction angle. In embodiments, whether other layers, such as a touch screen layer, are provided between the color filter layer  420  and the window  500  and whether an air layer is provided between the color filter layer  420  and the window  500  do not affect ‘L.’ Therefore, even when other layers, such as a touch screen layer, or the air layer is provided between the color filter layer  420  and the window  500 , as long as Inequality 9 is satisfied, the organic light-emitting display apparatus is within the scope of the present inventive concept. 
         [0068]    When ‘θ air  ’ is 90°, the organic light-emitting display apparatus has a very wide viewing angle. In this case, Inequality 9 may be modified as below in Inequality 10. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     n 
                                     air 
                                   
                                   
                                     n 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   
                                     n 
                                     air 
                                   
                                   
                                     n 
                                     CF 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Inequality 
                      
                     
                         
                     
                      
                     10 
                   
                   ] 
                 
               
             
           
         
       
     
         [0069]    Also, when the refraction index of air is equal to 1, Inequality 10 may be modified as below in Inequality 11. 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     ≥ 
                     
                       
                         
                           ∑ 
                           
                             i 
                             = 
                             1 
                           
                           m 
                         
                          
                         
                           
                             d 
                             i 
                           
                            
                           tan 
                            
                           
                             ? 
                           
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   1 
                                   
                                     n 
                                     i 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                       + 
                       
                         
                           d 
                           BM 
                         
                          
                         
                           tan 
                            
                           
                             ( 
                             
                               
                                 sin 
                                 
                                   - 
                                   1 
                                 
                               
                                
                               
                                 ( 
                                 
                                   1 
                                   
                                     n 
                                     CF 
                                   
                                 
                                 ) 
                               
                             
                             ) 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     
                       ? 
                     
                      
                     
                       indicates text missing or illegible when filed 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Inequality 
                      
                     
                         
                     
                      
                     11 
                   
                   ] 
                 
               
             
           
         
       
     
         [0070]    For example, supposing that, in the structure as shown in  FIG. 2 , the first and second inorganic encapsulating layers  310  and  330  include silicon oxide and each have a refraction index of 1.46 with respect to 550 nm wavelength light, the organic encapsulating layer  320  includes PET and has a refraction index of 1.65 with respect to 550 nm wavelength light, and the color filter layer  420  includes aluminum oxide and has a refraction index of 1.7 with respect to 550 nm wavelength light. Then, L may be as defined below in Inequality 12, wherein d 1  represents a thickness of the first inorganic encapsulating layer  310 , d 2  represents a thickness of the organic encapsulating layer  320 , and d 3  represents a thickness of the second inorganic encapsulating layer  330 . 
         [0000]      L≧0.94 d   1 +0.76 d   2 +0.94 d   3 +0.73d Bm    [Inequality 12]
 
         [0071]    Therefore, when d 1  is 1.5 μm, d 2  is 2.5 μm, d 3  is 1 μm, and d BM  is 2 μm, L has to be about 5.71 μm to prevent a decrease in light extraction efficiency. 
         [0072]    An inorganic encapsulating layer and an organic encapsulating layer may have different refraction indices according to wavelengths.  FIG. 3  is a graph of a refraction index according to wavelengths of silicon oxide, and  FIG. 4  is a graph of a refraction index according to wavelengths of silicon nitride. As shown in  FIGS. 3 and 4 , the refraction index of the inorganic encapsulating layer may vary according to wavelengths.  FIG. 5  is a graph of a refraction index according to wavelengths of polyacrylate, and  FIG. 6  is a graph of a refraction index according to wavelengths of PET. As shown in  FIGS. 5 and 6 , the refraction index of the organic encapsulating layer may vary according to wavelengths. This also applies to color filter layers. 
         [0073]    Therefore, when an organic light-emitting display apparatus includes a red sub-pixel, a blue sub-pixel, and a green sub-pixel, a minimum value of L that satisfies Inequality 9 may vary in each of the sub-pixels. Referring to  FIGS. 3 to 6 , in the case of silicon oxide, silicon nitride, polyacrylate, and PET, the refraction index may decrease as the wavelength increases. Based on the wavelength dependence of the refraction index in Inequality 9 or 11, the minimum value of L increases as the wavelength increases. Therefore, the green sub-pixel has a greater minimum value of L than the blue sub-pixel, and the red sub-pixel has a greater minimum value of L than the green sub-pixel. In embodiments, however, the distance L may be limited to an amount such that a portion of light-shielding layer  410  may be sufficiently formed between two immediately neighboring sub-pixels, although the invention is not limited thereto. 
         [0074]    By generalizing above embodiments, an organic light-emitting display apparatus according to the following embodiment is also within the scope of the present inventive concept, 
         [0075]    In embodiments, the organic light-emitting display apparatus according to the present embodiment includes an array of pixels, each of which includes first to third sub-pixels, an encapsulating layer on the first to third sub-pixels, a light-shielding layer on the encapsulating layer and corresponding to areas between the first to third sub-pixels, and a color filter layer on the encapsulating layer. The first sub-pixel includes a first light emission layer emitting first light having wavelength belonging to a first wavelength band, the second sub-pixel includes a second light emission layer emitting second light having wavelength belonging to a second wavelength band, and the third sub-pixel includes a third light emission layer emitting third light having wavelength belonging to a third wavelength band. Here, the wavelength of the second light is longer than wavelength of light belonging to the first wavelength band, and the wavelength of the third light is longer than wavelength of light belonging to the second wavelength band. For example, the first wavelength band may be 400-500 nm, the second wavelength band may be 500-600 nm, and the third wavelength band may be 600-1000 nm. Suppose that L 1  represents a distance between an edge of an emission area of the first light emission layer and a first edge of the light-shielding layer which defines a first hole of the light-shielding layer and surrounds the emission area of the first light emission layer when viewed along z-axis which may extend in a thickness direction of the apparatus. L 2  represents a distance between an edge of an emission area of the second light emission layer and a second edge of the light-shielding layer which defines a second hole of the light-shielding layer and surrounds the emission area of the second light emission layer when viewed along z-axis. L 3  represents a distance between an edge of an emission area of the third light emission layer and a third edge of the light-shielding layer which defines a third hole of the light-shielding layer and surrounds the emission area of the third light emission layer when viewed along z-axis. Then, as described above, based on the wavelength dependence of the refraction index in Inequality 9 or 11, L 1 &lt;L 2 &lt;L 3 . Thus, extraction efficiency of light generated by each of the first to third light emission layers may be substantially increased. 
         [0076]    While one or more embodiments have been described with reference to the figures, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope as defined by the following claims.