Abstract:
An organic EL display includes an organic EL element which includes first and second electrodes and an active layer interposed therebetween and including an emitting layer, and an outcoupling layer facing the first electrode. The organic EL element forms a waveguide layer which includes the first electrode and the active layer and in which light components from the emitting layer propagate in an in-plane direction while causing multiple-beam interference. A distance between the outcoupling layer and the waveguide layer is shorter than a wavelength of light from the organic EL element. A guide length x, a number of reflection m, an absorption coefficient α, and an outcoupling efficiency β satisfy a relationship represented by an inequality: 
     
       
         
           
             
               β 
               ⁢ 
               
                 
                   ∑ 
                   
                     M 
                     = 
                     1 
                   
                   m 
                 
                 ⁢ 
                 
                   
                     
                       ( 
                       
                         1 
                         - 
                         β 
                       
                       ) 
                     
                     
                       M 
                       - 
                       1 
                     
                   
                   
                     exp 
                     ⁢ 
                     
                       { 
                       
                         
                           α 
                           ⁡ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 M 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                         ⁢ 
                         x 
                       
                       } 
                     
                   
                 
               
             
             &gt; 
             
               0.1 
               .

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   This is a Continuation Application of PCT Application No. PCT/JP2005/017236, filed Sep. 13, 2005, which was published under PCT Article 21(2) in English. 
   This application is based upon and claims the benefit of priority from prior Japanese Patent Application No. 2004-276034, filed Sep. 22, 2004, the entire contents of which are incorporated herein by reference. 

   BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to an organic electroluminescent (EL) display. 
   2. Description of the Related Art 
   Since organic EL displays are of self-emission type, they have a wide viewing angle and a high repose speed. In addition, they do not require a backlight, and therefore, low-profile and lightweight are possible. For these reasons, the organic EL displays are attracting attention as a display which substitutes the liquid crystal display. 
   An organic EL element, which is the main part of the organic EL displays, includes a light-transmitting front electrode, a light-reflecting or light-transmitting back electrode facing the front electrode, and an organic layer interposed between the electrodes and containing a light-emitting layer. The organic EL element is a charge-injection type light-emitting element which emits light when an electric current flows through the organic layer. 
   In the meantime, the luminance of the organic EL element increases with the magnitude of current flowing through the EL element. However, if the current density is increased, power consumption increases and the lifetime of the organic EL element is significantly reduced. Therefore, in order to achieve high luminance, low power consumption, and long lifetime, it is important to more efficiently extract the light emitted by the organic element from the organic EL display, i.e., to improve an outcoupling efficiency. 
   BRIEF SUMMARY OF THE INVENTION 
   An object of the present invention is to improve an outcoupling efficiency of an organic EL display. 
   According to an aspect of the present invention, there is provided an organic EL display comprising an organic EL element which comprises a first electrode, a second electrode facing the first electrode, and an active layer interposed between the first and second electrodes and including an emitting layer, and an outcoupling layer facing the first electrode, wherein the organic EL element forms a waveguide layer which includes the first electrode and the active layer and in which light components from the emitting layer propagate in an in-plane direction parallel to a main surface of the waveguide layer while causing multiple-beam interference, wherein a distance between the outcoupling layer and the waveguide layer is shorter than a wavelength of light from the organic EL element, and wherein a guide length x in μm calculated by using a following equation (1), a number of reflection m calculated by using a following equation (2), an absorption coefficient α in μm −1  of the waveguide layer, and an outcoupling efficiency β of the outcoupling layer satisfy a relationship represented by a following inequality (3), where L is a thickness in pm of the waveguide layer, θ i  is an incident angle at which a light component with the highest intensity emitted by the emitting layer and propagating in the in-plane direction in the waveguide layer while causing multiple-beam interference is incident on a main surface of the waveguide layer facing the outcoupling layer, and the outcoupling efficiency β is a luminous energy ratio of a light component extracted from the waveguide layer with respect to an incident light for a single reflection of the light component with the highest intensity on the main surface of the waveguide layer facing the outcoupling layer. 
   
     
       
         
           
             
               
                 x 
                 = 
                 
                   L 
                   
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       i 
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
           
             
               
                 m 
                 = 
                 
                   
                     1 
                     2 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           100 
                         
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                       
                       + 
                       1 
                     
                     ) 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
           
             
               
                 
                   β 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         M 
                         = 
                         1 
                       
                       m 
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             β 
                           
                           ) 
                         
                         
                           M 
                           - 
                           1 
                         
                       
                       
                         exp 
                         ⁢ 
                         
                           { 
                           
                             
                               α 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     M 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             x 
                           
                           } 
                         
                       
                     
                   
                 
                 &gt; 
                 0.1 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
   

   
     BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING 
       FIG. 1  is a sectional view schematically showing an organic EL display according to a first embodiment of the present invention; 
       FIG. 2  is a view schematically showing how an outcoupling layer extracts light from a waveguide layer, in which the light propagates in an in-plane direction while causing multi-beam interference, to the atmosphere; 
       FIG. 3  is a view schematically showing how the light propagates in the waveguide layer in the in-plane direction while causing multi-beam interference; 
       FIG. 4  is a graph showing an example of a relationship between an absorption coefficient of the waveguide layer and a number of reflection; 
       FIG. 5  is a graph showing examples of a relationship between a number of reflection and an outcoupling efficiency; 
       FIG. 6  is a sectional view schematically showing an example of a structure which can be employed for an organic EL element of the organic EL display shown in  FIG. 1 ; and 
       FIG. 7  is a sectional view schematically showing another example of a structure which can be employed for an organic EL element of the organic EL display shown in  FIG. 1 . 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   An embodiment of the present invention will be described below in detail with reference to the accompanying drawings. The same reference numerals denote the same or similar constituent elements throughout the drawings, and a repetitive description thereof will be omitted. 
     FIG. 1  is a cross sectional view schematically showing an organic EL display according to an embodiment of the present invention. In  FIG. 1 , the organic EL display  1  is illustrated such that its display surface, that is, the front surface, faces downwardly and the back surface faces upwardly. 
   The organic EL display  1  is a top emission type organic EL display which employs an active matrix drive method. The organic EL display  1  includes an insulating substrate  10  such as a glass substrate. 
   On the transparent substrate  10 , pixels are arranged in a matrix form. Each pixel includes a pixel circuit and an organic EL element  40 . 
   The pixel circuit include, for example, a drive control element (not shown) and an output control switch  20  connected in series with the organic EL element  40  between a pair of power supply terminals, and pixel switch (not shown). The drive control element has a control terminal connected to a video signal line (not shown) via the pixel switch and outputs a current, whose magnitude corresponds to a video signal supplied from the video signal line, to the organic EL element  40  via the output control switch  20 . A control switch of the pixel switch is connected to a scan signal line (not shown), and a switching operation of the control switch is controlled by a scan signal supplied from the scan signal line. Note that other structures can be employed for the pixels. 
   On the substrate  10 , as an undercoat layer  12 , for example, an SiN x  layer and an SiO x  layer are arranged in this order. A semiconductor layer  13  such as a polysilicon layer in which a channel, source and drain are formed, a gate insulator  14  which can be formed with use of, for example, TEOS (tetraethyl orthosilicate), and a gate electrode  15  made of, for example, MoW, are arranged in this order on the undercoat layer  12 , and these layers form a top gate-type thin film transistor (referred to as a TFT hereinafter). In this example, the TFTs are used as TFTs of the pixel switch ST, output control switch and drive control element. Further, on the gate insulator  14 , scan signal lines (not shown) which can be formed in the same step as that for the gate electrode  15  are arranged. 
   An interlayer insulating film  17  made of, for example, SiO x  which is deposited by a plasma CVD method, covers the gate insulator  14  and gate electrode  15 . Source and drain electrodes  21  are arranged on the interlayer insulating film  17 , and they are buried in a passivation film  18  made of, for example, SiN x . The source and drain electrodes  21  have, for example, a three-layer structure of Mo/Al/Mo, and electrically connected to the source and drain of the TFT via contact holes formed in the interlayer insulating film  17 . Further, on the interlayer insulating film  17 , video signal lines (not shown) which can be formed in the same step as that for the source and drain electrodes  21  are arranged. 
   A flattening layer  19  is formed on the passivation film  18 . Reflection layers  70  are arranged on the flattening layer  19 . A hard resin can be used as a material of the flattening layer  19 , for example. A metal material such as Al, for example, can be used as a material of the reflection layer  70 . 
   The flattening layer  19  and the reflection layer  70  are covered with an outcoupling layer  30 . Here, as an example, the outcoupling layer  30  includes a first portion  31  with light-transmission property, and second portions  32  dispersed therein. For example, the second portions  32  have light-transmission property, and are different in refractive index from the first portion. 
   If an arrangement of the second portions  32  substantially forms a lattice when the outcoupling layer  30  is observed in a direction perpendicular to its film surface, the outcoupling layer  30  serves as a diffraction grating. Alternatively, if the second portions  32  are randomly arranged when the outcoupling layer  30  is observed in a direction perpendicular to that its film surface, the outcoupling layer  30  serves as a light-scattering layer. 
   The outcoupling layer  30  may not have a structure shown in  FIG. 1 . For example, the outcoupling layer  30  may be a film with light-transmission property which is provided with a number of recesses or protrusions on a main surface thereof. 
   On the outcoupling layer  30 , first electrodes  41  with light-transmission property are arranged spaced apart from one another. Each first electrode  41  faces the reflection layer  70 . In addition, each first electrode  41  is connected to a drain electrode  21  via through-holes formed in the passivation film  18 , the flattening layer  19 , and the outcoupling layer  30 . 
   The first electrode  41  is an anode in this example. As a material of the first electrode  41 , for example, a transparent conductive oxide such as an ITO (indium tin oxide) can be used. 
   A partition insulating layer  50  is placed on the outcoupling layer  30 . In the partition insulating layer  50 , through-holes are formed at positions corresponding to the first electrodes  41 . The partition insulating layer  50  is an organic insulating layer, for example, and can be formed by using a photolithography technique. 
   An active layer  42  including a light-emitting layer  42   a  is placed on each first electrode  41  which is exposed to a space in the through-hole of the partition insulating layer  50 . The light-emitting layer  42   a  is a thin film containing a luminescent organic compound which can generate a color of, for example, red, green or blue. The active layer  42  can further include a layer other than the light-emitting layer  42   a . For example, the active layer  42  can further include a buffer layer  42   b  which serves to mediate the injection of holes from the front electrode  41  into the emitting layer  42   a . The active layer  42  can further contain a hole transporting layer, a hole blocking layer, an electron transporting layer, an electron injection layer, etc. 
   The partition insulating layer  50  and the active layer  42  are covered with a second electrode  43  with light-transmission property. The second electrode  43  is a cathode which is continuously formed and common to all pixels. The second electrode  43  is electrically connected to an electrode wiring, the electrode wiring being formed on the layer on which video signal lines are formed, via contact holes (not shown) formed in the passivation film  18 , the flattening layer  19 , the outcoupling layer  30 , and the partition insulating layer  50 . Each organic EL element  40  includes the first electrode  41 , active layer  42  and second electrode  43 . 
   In general, the organic EL display  1  shown in  FIG. 1  are sealed by glass sealing or protective film sealing in order to prevent the organic EL elements  40  from being deteriorated due to contact with moisture or oxygen and the like. In addition, in general, a polarizing plate is placed on the front side of the organic EL elements  40 . 
   Although the organic EL display  1  shown in  FIG. 1  is of top emission type, the organic EL display  1  may be of bottom emission type. For example, the reflection layer  70  may be omitted, and the second electrode  43  may have light-reflection property. 
   As described above, in the organic EL display  1 , the outcoupling layer  30  is placed so as to be adjacent to the organic EL element  40 . When such a structure is employed, as described below, the light emitted by the light emitting layer  42   a  of the organic EL element  40  can be extracted from the organic EL display  1  with higher efficiency. 
   A portion of the light components emitted by the light emitting layer  42   a  propagates in an in-plane direction while repeating reflection (reflection or total reflection) in a region including the first electrode  41  and the active layer  42  of the organic EL element  40 , in this example, in a layered structure of the first electrode  41  and the active layer  42 . That is, a portion of the light components emitted by the light emitting layer  42   a  propagates in the in-plane direction while repeating reflection in a waveguide layer which includes the first electrode  41  and the active layer  42 . The light components propagating in the in-plane direction cannot be extracted from the waveguide layer if an incident angle on a main surface of the waveguide layer is great. 
   When the outcoupling layer  30  is placed adjacent to the organic EL element  40 , a direction of the light emitted by the light emitting layer  42   a  can be changed. Thus, it becomes possible to extract the light components emitted by the light emitting layer  42   a  from the organic EL display  1  with higher efficiency. 
   As described above, when the outcoupling layer  30  is used, luminous efficiency of the organic EL display  1  can be improved. However, a portion of the light components propagating in the waveguide layer in the in-plane direction is absorbed by the waveguide layer itself. 
   Therefore, in the present embodiment, the organic EL display  1  is designed as follows. That is, firstly, a guide length x (μm) is calculated in accordance with the following equation (1), in which L is a thickness (μm) of the waveguide layer, and θ i  is an incident angle at which a light component with the highest intensity emitted by the emitting layer  42   a  and propagating in the in-plane direction in the waveguide layer while causing multiple-beam interference is incident on a main surface of the waveguide layer facing the outcoupling layer  30 . Secondary, a number of reflection m is calculated in accordance with the following equation (2) using the guide length x (μm) and an absorption coefficient α (μm −1 ) of the waveguide layer. Thirdly, the organic EL display is designed such that the number of reflection m, the absorption coefficient α (μm −1 ), the guide length x (μm), and an outcoupling efficiency β of the outcoupling layer satisfy a relationship represented by the following inequality (3), where the outcoupling efficiency β is a luminous energy ratio of a light component extracted from the waveguide layer with respect to an incident light for a single reflection of the light component with the highest intensity on the main surface of the waveguide layer facing the outcoupling layer  30 . 
   
     
       
         
           
             
               
                 x 
                 = 
                 
                   L 
                   
                     cos 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       θ 
                       i 
                     
                   
                 
               
             
             
               
                 ( 
                 1 
                 ) 
               
             
           
           
             
               
                 m 
                 = 
                 
                   
                     1 
                     2 
                   
                   ⁢ 
                   
                     ( 
                     
                       
                         
                           ln 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           100 
                         
                         
                           α 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           x 
                         
                       
                       + 
                       1 
                     
                     ) 
                   
                 
               
             
             
               
                 ( 
                 2 
                 ) 
               
             
           
           
             
               
                 
                   β 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         M 
                         = 
                         1 
                       
                       m 
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             β 
                           
                           ) 
                         
                         
                           M 
                           - 
                           1 
                         
                       
                       
                         exp 
                         ⁢ 
                         
                           { 
                           
                             
                               α 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     M 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             x 
                           
                           } 
                         
                       
                     
                   
                 
                 &gt; 
                 0.1 
               
             
             
               
                 ( 
                 3 
                 ) 
               
             
           
         
       
     
   
   The outcoupling efficiency β and the number of reflection m will be described with reference to  FIGS. 2 and 3 . 
     FIG. 2  is a view schematically showing how an outcoupling layer extracts light from a waveguide layer, in which the light propagates in an in-plane direction while causing multi-beam interference, to the atmosphere. 
   In  FIG. 2 , a layered structure of the first electrode  41  and the active layer  42  is defined as a waveguide layer  140 . In addition, in  FIG. 2 , L 1   i  and L 1   r  indicate light with the highest intensity propagating in the in-plane direction in the waveguide layer  140  while causing multiple-beam interference, and L 2  indicates the light extracted from the waveguide layer  140  through the outcoupling layer  30  to the atmosphere when the light L 1   i  is incident on an interface between the waveguide layer and the outcoupling layer. 
   When the light L 1   i  is incident on the interface between the waveguide layer  140  and the outcoupling layer  30 , a portion of the light is extracted from the waveguide layer  140  to the atmosphere as light L 2 , and another portion is reflected as L 1   r . The outcoupling efficiency β is a value calculated from the following equation (4) concerning the light L 1   i  and the light L 2 . 
   
     
       
         
           
             
               
                 β 
                 = 
                 
                   
                     
                       ∫ 
                       0 
                       
                         2 
                         ⁢ 
                         π 
                       
                     
                     ⁢ 
                     
                       
                         ∫ 
                         0 
                         
                           π 
                           / 
                           2 
                         
                       
                       ⁢ 
                       
                         
                           i 
                           ⁡ 
                           
                             ( 
                             
                               θ 
                               , 
                               ϕ 
                             
                             ) 
                           
                         
                         ⁢ 
                         
                           ⅆ 
                           θ 
                         
                         ⁢ 
                         
                           ⅆ 
                           ϕ 
                         
                       
                     
                   
                   
                     I 
                     0 
                   
                 
               
             
             
               
                 ( 
                 4 
                 ) 
               
             
           
         
       
     
   
   In equation (4) above, I 0  indicates a luminous energy of incident light L 1   i . In addition, i(θ,φ) indicates a luminous energy of light components of the light L 2  which travel in a direction defined by a polar angle θ and a cone angle φ when the polar axis is parallel to the film surface. 
     FIG. 3  is a view schematically showing how the light propagates in the waveguide layer in the in-plane direction while causing multi-beam interference. In  FIG. 3 , L 1  indicates a light component with the highest intensity of the light propagating in the in-plane direction while causing multiple-beam interference in the waveguide layer  140 . 
   As shown in  FIG. 3 , the guide distance x (μm) is a length of a line segment which is parallel to the traveling direction of the light L 1  and extends from one main surface to the other main surface of the waveguide layer  140 . In the case of ignoring decrease in luminous energy of the light L 1  due to reflection, a luminous energy I 1   M  of the light L 1  reflected M times on the interface between the waveguide layer  140  and the outcoupling layer  30  can be calculated from the following equation (5), in which M is a number of reflection of the light L 1  on the interface between the waveguide layer  140  and the outcoupling layer  30 , α (μm −1 ) is an absorption coefficient of the waveguide layer  140  concerning the light L 1 , and I 0  is an initial luminous energy of the light L 1 . 
   
     
       
         
           
             
               
                 
                   I 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     1 
                     M 
                   
                 
                 = 
                 
                   
                     I 
                     0 
                   
                   
                     exp 
                     ⁢ 
                     
                       { 
                       
                         
                           α 
                           ⁡ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 M 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                         ⁢ 
                         x 
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 5 
                 ) 
               
             
           
         
       
     
   
   A number of reflection m corresponds to the number M in the equation (5) when the luminous energy I 1   M  is one hundredth of the luminous energy I 0 . That is, the number of reflection m is a total number of reflection on the interface between the waveguide layer  140  and the outcoupling layer  30  until the luminous energy of the light L 1  is decreased to one hundredth of the initial luminous energy. 
     FIG. 4  is a graph showing an example of a relationship between the absorption coefficient α of the waveguide layer and the number of reflection m. In the figure, the abscissa indicates the absorption coefficient α, and the ordinate indicates the number of reflection m. 
     FIG. 4  shows data in the case where the thickness L of the waveguide layer is 0.21 μm, and an incident angle θ i  is 60°. As shown in  FIG. 4 , in the case where the absorption coefficient α is 0.5 μm −1 , the number of reflection m is 12. 
   Based on the foregoing, the luminous energy I 2   M  of the light L 2  extracted from the waveguide layer  140  to the atmosphere at the time of an M-th reflection of the light L 1  on the interface between the waveguide layer  140  and the outcoupling layer  30  can be calculated from the following equation (6). 
   
     
       
         
           
             
               
                 
                   I 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   
                     2 
                     M 
                   
                 
                 = 
                 
                   
                     
                       I 
                       0 
                     
                     ⁢ 
                     
                       
                         β 
                         ⁡ 
                         
                           ( 
                           
                             1 
                             - 
                             β 
                           
                           ) 
                         
                       
                       
                         M 
                         - 
                         1 
                       
                     
                   
                   
                     exp 
                     ⁢ 
                     
                       { 
                       
                         
                           α 
                           ⁡ 
                           
                             ( 
                             
                               
                                 2 
                                 ⁢ 
                                 M 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                         ⁢ 
                         x 
                       
                       } 
                     
                   
                 
               
             
             
               
                 ( 
                 6 
                 ) 
               
             
           
         
       
     
   
   Therefore, a total luminous energy ΣI 2   M  of the light L 2  extracted from the waveguide layer  140  to the atmosphere when the light L 1  is reflected n-times on the interface between the waveguide layer  140  and the outcoupling layer  30  can be calculated from the following equation (7). 
   
     
       
         
           
             
               
                 
                   
                     ∑ 
                     
                       M 
                       = 
                       1 
                     
                     n 
                   
                   ⁢ 
                   
                     I 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       2 
                       M 
                     
                   
                 
                 = 
                 
                   
                     I 
                     0 
                   
                   ⁢ 
                   β 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         M 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             β 
                           
                           ) 
                         
                         
                           M 
                           - 
                           1 
                         
                       
                       
                         exp 
                         ⁢ 
                         
                           { 
                           
                             
                               α 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     M 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             x 
                           
                           } 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 7 
                 ) 
               
             
           
         
       
     
   
   Therefore, a ratio of the total luminous energy ΣI 2   M  of the light L 2  when the light L 1  is reflected n-times on the interface between the waveguide layer  140  and the outcoupling layer  30  with respect to the initial luminous energy I 0 , i.e., the outcoupling efficiency, ΣI 2   M /I 0  can be calculated from the following equation (8). 
   
     
       
         
           
             
               
                 
                   
                     ∑ 
                     
                       M 
                       = 
                       1 
                     
                     n 
                   
                   ⁢ 
                   
                     I 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         2 
                         M 
                       
                       / 
                       
                         I 
                         0 
                       
                     
                   
                 
                 = 
                 
                   β 
                   ⁢ 
                   
                     
                       ∑ 
                       
                         M 
                         = 
                         1 
                       
                       n 
                     
                     ⁢ 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             β 
                           
                           ) 
                         
                         
                           M 
                           - 
                           1 
                         
                       
                       
                         exp 
                         ⁢ 
                         
                           { 
                           
                             
                               α 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     2 
                                     ⁢ 
                                     M 
                                   
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                             ⁢ 
                             x 
                           
                           } 
                         
                       
                     
                   
                 
               
             
             
               
                 ( 
                 8 
                 ) 
               
             
           
         
       
     
   
     FIG. 5  is a graph showing examples of a relationship between the number of reflection n and the outcoupling efficiency ΣI 2   M /I 0 . In the figure, the abscissa indicates the number of reflection n, and the ordinate indicates the outcoupling efficiency ΣI 2   M /I 0 . In addition,  FIG. 5  shows data in the case where the thickness L of the waveguide layer is 0.21 μm, an incident angle θ i  is 60°, an absorption coefficient α is 0.5 μm −1 , and outcoupling efficiency β is 0.01, 0.05, 0.1, 0.2, or 0.3. 
   As shown in  FIG. 5 , a change in the outcoupling ratio ΣI 2   M /I 0  in accordance with an increase of the number of reflection n is slowed down when the number of reflection n is 5 or more, and substantially saturates when the number of reflection n is about 12. 
   In addition, as the outcoupling efficiency β increases, the outcoupling ratio ΣI 2   M /I 0  also increases. In particular, in the case where the outcoupling efficiency β is 0.05 or more, if the number of reflection n is 5 or more, an outcoupling ratio ΣI 2   M /I 0  of 10% or more can be achieved. 
   As is evident from the foregoing, when the organic EL display  1  is designed so as to meet the relationship represented by the inequality (3), it becomes possible to more efficiently extract the light propagating in the in-plane direction from the waveguide layer  140 . That is, the light outcoupling efficiency of the organic EL display  1  can be improved. 
   Although the foregoing description considers only attenuation of light L 1  due to absorption of the waveguide layer  140 , in actuality, the light L 1  is attenuated by being reflected on the interface between the waveguide layer  140  and the second electrode  43 . When attenuation of the light L 1  caused by reflection on this interface is restricted, the outcoupling efficiency of the organic EL display  1  can be further improved. 
     FIG. 6  is a sectional view schematically showing an example of a structure which can be employed for the organic EL element of the organic EL display shown in  FIG. 1 .  FIG. 7  is a sectional view schematically showing another example of a structure which can be employed for the organic EL element of the organic EL display shown in  FIG. 1 . The organic EL element  40  shown in  FIG. 6  and the organic EL element  40  shown in  FIG. 7  have the same structure except for the second electrode  43  as a cathode. 
   In each organic EL element  40  of  FIGS. 6 and 7 , the first electrode  41  which is an anode includes an ITO layer  41   a  and an amorphous carbon layer  41   b . The thickness of the ITO layer  41  is 50 nm, for example, and the thickness of the amorphous carbon layer  41   b  is 3 nm, for example. 
   In the organic EL element  40  of  FIGS. 6 and 7 , the active layer  42  includes the light emitting layer  42   a , a TPT layer  42   b , a BAlq layer  42   c , and an Alq 3  layer  42   d . Note that the “TPT” is tetraphenylthiophene, Alq 3  is an aluminum complex in which three oxines coordinate with an aluminum atom, and BAlq is obtained by substituting one of quinolate ligands of Al q3  by phenolate. For example, the thickness of the light emitting layer  42   a  is 30 nm, and the thickness of the TPT layer  42   b  is 90 nm. In addition, for example, the thickness of the BAlq layer is 10 nm, and the thickness of the Al q3  layer is 40 nm. 
   In the organic EL element  40  of  FIG. 6 , the second electrode  42  which is a cathode includes an ITO layer  43   a , an MgAg layer  43   b , and an LiF layer  43   c . For example, the thickness of the ITO layer  43   a  is 50 nm, the thickness of the MgAg layer  43   b  is 10 nm, and the thickness of the LiF layer is 1 nm. 
   On the other hand, in the organic EL element  40  of  FIG. 7 , the second electrode  42  which is a cathode includes an ITO layer  43   a , an Ag layer  43   d , an MgAg layer  43   b , and an LiF layer  43   c . In the organic element  40  of  FIG. 7 , for example, the thickness of the ITO layer  43   a  is 50 nm, the thickness of the Ag layer  43   d  is 5 nm, the thickness of the MgAg layer  43   b  is 5 nm, and the thickness of the LiF layer is 1 nm. In this way, the organic EL element  40  of  FIG. 7  is different from the organic element  40  of  FIG. 6  in that the Ag layer  43   d  is added to the second electrode  42  and the MgAg layer  43   b  is thinner. 
   An MgAg alloy is excellent as an electron injection layer. However, the MgAg alloy is comparatively large in light absorption. 
   In the organic EL element  40  of  FIG. 6 , if the MgAg layer  43   b  is thinner, light absorption by the second electrode  43  can be reduced. However, if the MgAg layer  43   b  is thin, an underlayer below the MgAg layer  43   b  is damaged when the ITO layer  43   a  is formed on the MgAg layer. 
   In the organic EL element  40  of  FIG. 7 , the Ag layer  43   d  is placed between the MgAg layer  43   b  and the ITO layer  43   a . Ag is smaller in light absorption as compared with the MgAg alloy. In addition, the Ag layer  43   d  prevents the undercoat from being damaged when the ITO layer  43   a  is deposited. That is, when the structure of  FIG. 7  is employed, light absorption by the second electrode  43  can be reduced as compared with a case in which the structure of  FIG. 6  is employed. Moreover, it becomes possible to prevent the undercoat from being damaged when the ITO layer  43   a  is deposited. 
   Such effects can be attained by another method. For example, in the organic EL element  40  of  FIG. 6 , an Ag content in the MgAg layer  43   b  may be increased. For example, the Ag content may increased from 7% to 50%. By doing this, light absorption by the second electrode  43  can be reduced. 
   Note that an amorphous carbon is a material whose light absorption is comparatively large. Therefore, it is desirable that an amorphous carbon layer  41   b  be thinly formed. 
   In addition, instead of the MgAg layer, for example, there may be used an organic substance layer doped with an alkaline metal element and/or an alkaline earth metal element, for example. For example, a layer of Alq 3  doped with Cs may be used. In this manner, it becomes possible to ensure transparency of a light-transmission electrode. 
   While the above embodiment has described a case of placing the outcoupling layer on the back side of the organic EL element by way of example, the outcoupling layer may be placed on the front side of the organic EL element. 
   The outcoupling layer may employ another construction. For example, the outcoupling layer may employ a diffraction grating structure. The display may further include a flattening film for flattening irregularities on a surface of the outcoupling layer. 
   While the above embodiment has described a top emission structure, a bottom emission structure can be employed. When a bottom emission structure is employed, by using Ag as a material of a light-reflection upper electrode, absorption of light by a layer adjacent to a waveguide layer can be decreased as compared with the case where Al is used as the material. 
   As has been described above, when the layer adjacent to the waveguide layer is made of a material having low light absorption, attenuation of light in the waveguide layer can be suppressed. 
   In addition, in a display utilizing a reflection layer, by placing a material whose refractive index is lower than that of an organic layer or a transparent electrode and whose absorption is low between the reflection layer and the transparent electrode, attenuation of light in the waveguide layer can be suppressed. 
   In addition, by decreasing a thickness of a layer with large absorption coefficient included in the organic layer or by replacing the layer with large absorption coefficient by a transparent layer attenuation of light in the waveguide layer can be suppressed. 
   Additional advantages and modifications will readily occur to those skilled in the art. Therefore, the invention in its broader aspects is not limited to the specific details and representative embodiments shown and described herein. Accordingly, various modifications may be made without departing from the spirit or scope of the general inventive concept as defined by the appended claims and their equivalents.