Abstract:
An element substrate is provided, including a substrate, a metal layer and a planarization layer. The metal layer is located on the substrate. The metal layer has a first edge in a first direction. The planarization layer is located on the metal layer. The planarization layer includes a contact hole. The contact hole has a contiguous wall and a bottom side. The metal layer is exposed in the bottom side. A contour line of the contiguous wall on a vertical plane is a curved line. The first edge corresponds vertically with a critical point on the contour line. The slope of a tangent line on the critical point of the contour line is smaller than 0.176.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This Application claims priority of Taiwan Patent Application No. 103124494, filed on Jul. 17, 2014, the entirety of which is incorporated by reference herein. 
       BACKGROUND OF THE INVENTION 
       [0002]    1. Field of the Invention 
         [0003]    The present invention relates to a liquid-crystal display, and in particular to a liquid-crystal display having at least one contact hole. 
         [0004]    2. Description of the Related Art 
         [0005]    In a liquid-crystal display, a contact hole is utilized to conduct a pixel electrode and a source electrode. However, with reference to  FIG. 1 , the liquid-crystal molecules  2  are arranged along a profile of the contact hole  1 . The contact hole  1  is like a funnel structure, and light leakage happens due to the liquid-crystal molecules  2  arranged along the profile of the contact hole  1 , and the contrast of the liquid-crystal display is decreased. 
         [0006]    With reference to  FIG. 1 , conventionally, an area of the source electrode  3  at the bottom the contact hole  1  is increased to cover the light-leaking liquid-crystal molecules  2 , and to improve the contrast of the liquid-crystal display. However, this method decreases the aperture ratio and the illumination of the liquid-crystal display, and an improved solution is required. 
       BRIEF SUMMARY OF THE INVENTION 
       [0007]    In one embodiment of the invention, an element substrate is provided, which includes a substrate, a metal layer and a planarization layer. The metal layer is disposed on the substrate, wherein the metal layer has a first width along a first direction. The planarization layer is located on the metal layer, wherein the planarization layer comprises a contact hole, the contact hole has a contiguous wall and a bottom, the bottom exposes the metal layer, and the bottom of the contact hole has a second width along the first direction, wherein the first width and the second width satisfy the following equation: 
         [0000]    
       
         
           
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               p 
                             
                             ) 
                           
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               p 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               
                                 - 
                                 0.176 
                               
                               * 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   p 
                                 
                                 ) 
                               
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               - 
               1.8 
             
             ≤ 
             
               L 
               1 
             
             ≤ 
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               p 
                             
                             ) 
                           
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               p 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               
                                 - 
                                 0.176 
                               
                               * 
                               
                                 ( 
                                 
                                   1 
                                   - 
                                   p 
                                 
                                 ) 
                               
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   p 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               + 
               1.8 
             
           
         
       
     
         [0000]    wherein L 1  is the first width along the first direction, and L 2  is the second width along the first direction, h is a thickness of the planarization layer, and θ is an included angle between a straight line and a extension surface of the bottom, and the straight line connects a reference point and a base point, and the reference point and the base point are located on the contiguous wall, wherein the vertical distance from the reference point to the substrate is 0.95 h. The base point is located at the point where the contiguous wall is connected to the bottom, p is an adjustable parameter, and (1-p)h is the height of the reference point in a vertical direction, and 0&lt;p≦0.1. 
         [0008]    Utilizing the embodiment of the invention, the aperture ratio and the light transmittance (the contrast in dark state) of the liquid-crystal display are optimized, and the light leakage and the low-contrast problem are prevented. 
         [0009]    A detailed description is given in the following embodiments with reference to the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0010]    The present invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein: 
           [0011]      FIG. 1  shows an element substrate of a conventional liquid-crystal display; 
           [0012]      FIG. 2  shows an element substrate of an embodiment of the invention; 
           [0013]      FIG. 3A  shows the element substrate of the embodiment of the invention utilized in a liquid-crystal display; 
           [0014]      FIG. 3B  shows the structure of portion  3 B of  FIG. 3A  in detail; 
           [0015]      FIG. 4  shows an element substrate of a modified embodiment of the invention; 
           [0016]      FIG. 5  shows a liquid-crystal display of an embodiment of the invention; and 
           [0017]      FIG. 6  shows the designed width and the actual width of the metal layer. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0018]    The following description is of the best-contemplated mode of carrying out the invention. This description is made for the purpose of illustrating the general principles of the invention and should not be taken in a limiting sense. The scope of the invention is best determined by reference to the appended claims. 
         [0019]      FIG. 2  shows an element substrate  100  of an embodiment of the invention, which comprises a substrate  110 , a metal layer  120  and a planarization layer  130 . The metal layer  120  is disposed on the substrate  110 , wherein the metal layer  120  has a first width L 1  along a first direction X. The planarization layer  130  is located on the metal layer  120 , wherein the planarization layer  130  comprises a contact hole  131 , the contact hole  131  has a contiguous wall  132  and a bottom  133 , the bottom  133  exposes the metal layer  120 , and the bottom  133  of the contact hole  131  has a second width L 2  along the first direction X. 
         [0020]    The applicant has discovered that the liquid-crystal molecules are arranged along the contiguous wall  132 , and the light transmittance (the contrast in dark state) is changed with the slope of the contiguous wall  132 . At the location where the tangent slope of the contiguous wall  132  is about tan 10°, light leakage is acceptable, and the contrast of the liquid-crystal display is qualified. When the edge of the metal layer  120  extends to the critical point  136  (where the tangent slope of the contiguous wall  132  is about tan 10°), the aperture ratio and the light transmittance (the contrast in dark state) are optimized. 
         [0021]    With reference to  FIG. 2 , the applicant has discovered from deriving curve equations that when the first width and the second width satisfy the following equation, the aperture ratio and the light transmittance (the contrast in dark state) are optimized: 
         [0000]    
       
         
           
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.95 
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               - 
                               0.1672 
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               - 
               1.8 
             
             ≤ 
             
               L 
               1 
             
             ≤ 
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.95 
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               - 
                               0.1672 
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               + 
               1.8 
             
           
         
       
     
         [0000]    wherein L 1  is the first width of the metal layer  120  along the first direction X, and L 2  is the second width of the bottom  133  of the contact hole  131  along the first direction X, h is the thickness of the planarization layer  130 , 0  is an included angle between a straight line L and a extension surface of the bottom  133 . The straight line L connects a reference point  134  and a base point  135 , the reference point  134  and the base point  135  are located on the contiguous wall  132 , wherein the vertical distance from the reference point  134  to the substrate is 0.95 h. The base point  135  is located at the point where the contiguous wall  132  is connected to the bottom  133 , and ±1.8 is the tolerance. By modifying the parameters above, the curvature and the shape of the contiguous wall  132  can be modified. 
         [0022]    With reference to  FIG. 2 , the derivative of the curve equation is presented in the following description. 
         [0023]    First, curve fitting (assuming), assuming a curve equation of the contiguous wall of the contact hole is: 
         [0000]        y=f ( x )=− A ′ exp(− x )   (1)
 
         [0024]    In equation (1), only asymptotes of the contiguous wall are defined, and the equation (1) must be regulated relative to X axis and Y axis. 
         [0025]    Next, the curve fitting (relative to reference point  134 , base point  135  and included angle θ), assuming that a distance between the reference point  134  and the top of the planarization layer  130  is p times of the thickness h of the planarization layer  130 , and satisfies equation f(R′), and the horizontal distance between the reference point  134  and the base point  135  is R′, then: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                        
                       
                         ( 
                         
                           R 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         - 
                         ph 
                       
                       = 
                       
                         
                           
                             
                               - 
                               h 
                             
                              
                             
                                 
                             
                              
                             
                               exp 
                                
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       R 
                                       ′ 
                                     
                                   
                                   α 
                                 
                                 ) 
                               
                             
                           
                           ⇒ 
                           α 
                         
                         = 
                         
                           
                             - 
                             
                               R 
                               ′ 
                             
                           
                           
                             ln 
                              
                             
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                     &gt; 
                     0 
                   
                   , 
                   
                     h 
                     &gt; 
                     0 
                   
                   , 
                   
                     
                       R 
                       ′ 
                     
                     &gt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
         [0026]    Correction parameter a is achieved. 
         [0027]    Next, a straight line L connects the reference point  134  and the base point  135 , and an included angle between a straight line and the horizontal line is 0, then: 
         [0000]    
       
         
           
             
               
                 
                   
                     tan 
                      
                     
                         
                     
                      
                     θ 
                   
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               p 
                             
                             ) 
                           
                            
                           h 
                         
                         
                           R 
                           ′ 
                         
                       
                       ⇒ 
                       
                         R 
                         ′ 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             p 
                           
                           ) 
                         
                          
                         h 
                       
                       
                         tan 
                          
                         
                             
                         
                          
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
     
         [0028]    Material property 0 is brought in. 
         [0029]    Next, the vertical distance between the reference point and the substrate is 0.95 h. By combining equations of equation (2) and equation (3), we get: 
         [0000]    
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       
                         - 
                         
                           R 
                           ′ 
                         
                       
                       
                         ln 
                          
                         
                           ( 
                           0.05 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           - 
                           0.95 
                         
                          
                         h 
                       
                       
                         
                           
                             ln 
                              
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           tan 
                         
                          
                         
                             
                         
                          
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
         [0030]    Correction parameter α is achieved. 
         [0031]    Next, the included angle β between a cut line L′ at base point  135  and the horizontal line defines the angle of the curve of the planarization layer  130 , and included angle β substantially equals 1.50. Therefore, by revising the curve equation (angle revising) further, we get: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           f 
                            
                           
                             ( 
                             
                               R 
                               ′ 
                             
                             ) 
                           
                         
                         = 
                           
                          
                         
                           
                             
                               
                                 - 
                                 h 
                               
                               · 
                               exp 
                             
                              
                             
                               { 
                               
                                 
                                   - 
                                   
                                     R 
                                     ′ 
                                   
                                 
                                 / 
                                 α 
                               
                               } 
                             
                           
                           = 
                           
                             
                               
                                 - 
                                 h 
                               
                               · 
                               exp 
                             
                              
                             
                               { 
                               
                                 
                                   R 
                                   ′ 
                                 
                                 · 
                                 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       tan 
                                     
                                      
                                     
                                         
                                     
                                      
                                     β 
                                   
                                   
                                     0.95 
                                      
                                     h 
                                   
                                 
                               
                               } 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             
                               - 
                               h 
                             
                             · 
                             exp 
                           
                            
                           
                             { 
                             
                               
                                 R 
                                 ′ 
                               
                               · 
                               
                                 
                                   
                                     ln 
                                      
                                     
                                       ( 
                                       0.05 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     tan 
                                      
                                     
                                       ( 
                                       
                                         1.5 
                                          
                                         θ 
                                       
                                       ) 
                                     
                                   
                                 
                                 
                                   0.95 
                                    
                                   h 
                                 
                               
                             
                             } 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
         [0032]    Curve equation of the contact hole is achieved. 
         [0033]    Next, R=Ro+R′, by bringing this equation into the above equation, we get: 
         [0000]    
       
         
           
             
               
                 
                   
                     ∵ 
                     
                       R 
                       ′ 
                     
                   
                   = 
                   
                     
                       
                         R 
                         - 
                         
                           
                             R 
                             0 
                           
                            
                           
                               
                           
                            
                           … 
                            
                           
                               
                           
                            
                           
                             ( 
                             shifting 
                             ) 
                           
                         
                       
                       ⇒ 
                       
                         f 
                          
                         
                           ( 
                           
                             R 
                             ′ 
                           
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           
                             - 
                             h 
                           
                           · 
                           exp 
                         
                          
                         
                           { 
                           
                             
                               - 
                               
                                 ( 
                                 
                                   R 
                                   - 
                                   
                                     R 
                                     0 
                                   
                                 
                                 ) 
                               
                             
                             / 
                             α 
                           
                           } 
                         
                       
                       = 
                       
                         
                           
                             - 
                             h 
                           
                           · 
                           exp 
                         
                          
                         
                           { 
                           
                             
                               ( 
                               
                                 R 
                                 - 
                                 
                                   R 
                                   0 
                                 
                               
                               ) 
                             
                             · 
                             
                               
                                 
                                   ln 
                                    
                                   
                                     ( 
                                     0.05 
                                     ) 
                                   
                                 
                                 · 
                                 
                                   tan 
                                    
                                   
                                     ( 
                                     
                                       1.5 
                                        
                                       θ 
                                     
                                     ) 
                                   
                                 
                               
                               
                                 0.95 
                                  
                                 h 
                               
                             
                           
                           } 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
         [0034]    Actual curve equation of the contact hole is achieved. 
         [0035]    Next, as mentioned above, at the location where the tangent slope of the contiguous wall  132  is about tan10 °, the light leakage is acceptable, and the contrast of the liquid-crystal display is qualified. When the edge of the metal layer  120  extends to the critical point  136  (where the tangent slope of the contiguous wall  132  is about tan 10°), and the aperture ratio and the light transmittance (dark state contrast) are optimized. The equation of half of the second width of the metal layer along the first direction is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         f 
                          
                         
                           ( 
                           
                             R 
                             ′ 
                           
                           ) 
                         
                       
                     
                     
                       ∂ 
                       
                         R 
                         ′ 
                       
                     
                   
                   = 
                   
                     
                       tan 
                        
                       
                           
                       
                        
                       10 
                        
                       ° 
                     
                     = 
                     
                       0.176 
                       = 
                       
                         
                           
                             
                               
                                 ∂ 
                                 
                                     
                                 
                               
                               
                                 ∂ 
                                 
                                   R 
                                   ′ 
                                 
                               
                             
                              
                             
                               { 
                               
                                 
                                   - 
                                   h 
                                 
                                 · 
                                 
                                   exp 
                                    
                                   
                                     [ 
                                     
                                       
                                         R 
                                         ′ 
                                       
                                       · 
                                       
                                         
                                           
                                             ln 
                                              
                                             
                                               ( 
                                               0.05 
                                               ) 
                                             
                                           
                                           · 
                                           
                                             tan 
                                              
                                             
                                               ( 
                                               
                                                 1.5 
                                                  
                                                 θ 
                                               
                                               ) 
                                             
                                           
                                         
                                         
                                           0.95 
                                            
                                           h 
                                         
                                       
                                     
                                     ] 
                                   
                                 
                               
                               } 
                             
                           
                           ⇒ 
                           
                             
                               - 
                               h 
                             
                             · 
                             
                               exp 
                                
                               
                                 [ 
                                 
                                   
                                     R 
                                     ′ 
                                   
                                   · 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                          
                                         
                                           ( 
                                           
                                             1.5 
                                              
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       0.95 
                                        
                                       h 
                                     
                                   
                                 
                                 ] 
                               
                             
                             · 
                             
                               
                                 
                                   ∂ 
                                   
                                       
                                   
                                 
                                 
                                   ∂ 
                                   
                                     R 
                                     ′ 
                                   
                                 
                               
                                
                               
                                 [ 
                                 
                                   
                                     R 
                                     ′ 
                                   
                                   · 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                          
                                         
                                           ( 
                                           
                                             1.5 
                                              
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       0.95 
                                        
                                       h 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         = 
                         
                           
                             0.176 
                             ⇒ 
                             
                               exp 
                                
                               
                                 [ 
                                 
                                   
                                     R 
                                     ′ 
                                   
                                   · 
                                   
                                     
                                       
                                         ln 
                                          
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                          
                                         
                                           ( 
                                           
                                             1.5 
                                              
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       0.95 
                                        
                                       h 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           = 
                           
                             
                               
                                 
                                   
                                     - 
                                     0.176 
                                   
                                   · 
                                   0.95 
                                 
                                 
                                   
                                     ln 
                                      
                                     
                                       ( 
                                       0.05 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     tan 
                                      
                                     
                                       ( 
                                       
                                         1.5 
                                          
                                         θ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ⇒ 
                               
                                 
                                   R 
                                   ′ 
                                 
                                 · 
                                 
                                   
                                     
                                       ln 
                                        
                                       
                                         ( 
                                         0.05 
                                         ) 
                                       
                                     
                                     · 
                                     
                                       tan 
                                        
                                       
                                         ( 
                                         
                                           1.5 
                                            
                                           θ 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     0.95 
                                      
                                     h 
                                   
                                 
                               
                             
                             = 
                             
                               
                                 
                                   ln 
                                    
                                   
                                     [ 
                                     
                                       
                                         - 
                                         0.1672 
                                       
                                       
                                         
                                           ln 
                                            
                                           
                                             ( 
                                             0.05 
                                             ) 
                                           
                                         
                                         · 
                                         
                                           tan 
                                            
                                           
                                             ( 
                                             
                                               1.5 
                                                
                                               θ 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                                 ⇒ 
                                 
                                   R 
                                   ′ 
                                 
                               
                               = 
                               
                                 
                                   
                                     
                                       
                                         0.95 
                                          
                                         h 
                                       
                                       
                                         
                                           ln 
                                            
                                           
                                             ( 
                                             0.05 
                                             ) 
                                           
                                         
                                         · 
                                         
                                           tan 
                                            
                                           
                                             ( 
                                             
                                               1.5 
                                                
                                               θ 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     · 
                                     
                                       ln 
                                        
                                       
                                         [ 
                                         
                                           
                                             - 
                                             0.1672 
                                           
                                           
                                             
                                               ln 
                                                
                                               
                                                 ( 
                                                 0.05 
                                                 ) 
                                               
                                             
                                             · 
                                             
                                               tan 
                                                
                                               
                                                 ( 
                                                 
                                                   1.5 
                                                    
                                                   θ 
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                   
                                   ⇒ 
                                   R 
                                 
                                 = 
                                 
                                   
                                     R 
                                     0 
                                   
                                   + 
                                   
                                     
                                       
                                         0.95 
                                          
                                         h 
                                       
                                       
                                         
                                           ln 
                                            
                                           
                                             ( 
                                             0.05 
                                             ) 
                                           
                                         
                                         · 
                                         
                                           tan 
                                            
                                           
                                             ( 
                                             
                                               1.5 
                                                
                                               θ 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     · 
                                     
                                       ln 
                                        
                                       
                                         [ 
                                         
                                           
                                             - 
                                             0.1672 
                                           
                                           
                                             
                                               ln 
                                                
                                               
                                                 ( 
                                                 0.05 
                                                 ) 
                                               
                                             
                                             · 
                                             
                                               tan 
                                                
                                               
                                                 ( 
                                                 
                                                   1.5 
                                                    
                                                   θ 
                                                 
                                                 ) 
                                               
                                             
                                           
                                         
                                         ] 
                                       
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
         [0036]    Considering that ±1.8 is acceptable manufacturing tolerance, when the first width and the second width satisfy the following equation, the aperture ratio and the light transmittance (dark state contrast) are optimized: 
         [0000]    
       
         
           
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.95 
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               - 
                               0.1672 
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               - 
               1.8 
             
             ≤ 
             
               L 
               1 
             
             ≤ 
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.95 
                            
                           h 
                         
                         
                           
                             ln 
                              
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           
                             tan 
                              
                             
                               ( 
                               
                                 1.5 
                                  
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                          
                         
                           [ 
                           
                             
                               - 
                               0.1672 
                             
                             
                               
                                 ln 
                                  
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                  
                                 
                                   ( 
                                   
                                     1.5 
                                      
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               + 
               1.8 
             
           
         
       
     
         [0037]    In one embodiment, the included angle θ is between 20˜40 degrees, such as between 25˜35 degrees. 
         [0038]    With reference to  FIG. 2 , the element substrate  100  further comprises a conductive layer  140  disposed on the planarization layer  130 , wherein the conductive layer  140  is electrically connected to the metal layer  120  via the contact hole  131 . The conductive layer  140  is a made of transparent material or metal. 
         [0039]    In one embodiment, the metal layer is a source electrode or a drain electrode of a driving element. In one embodiment, the element substrate  100  further comprises a semiconductor layer  137  located between the metal layer  120  and the substrate  110 . The semiconductor layer  137  can be made of polycrystalline silicon, noncrystalline silicon or metal oxide. 
         [0040]      FIG. 3A  shows the element substrate of the embodiment of the invention utilized in a liquid-crystal display  200 , which comprises a active area (pixel area) A and an non-active area (B).  FIG. 3B  shows detailed structures of portion  3 B is  FIG. 3A , wherein the liquid-crystal display  200  further comprises scan lines  201 , data lines  202 , a semiconductor layer  203 , source electrodes  240 , a contact hole  231 , a bottom  233  of the contact hole, drain electrodes  204 , common electrodes  205  and pixel electrodes  210 , which are located in the active area A. In an embodiment of the invention, the metal layer  120  comprises the source electrodes  240 , the drain electrodes  204 , the scan lines  201  and the signal lines  202 . 
         [0041]    With reference to  FIG. 2 , in another embodiment, the metal  120  comprises a first edge  121  along the first direction X, the first edge  121  vertically corresponds to a critical point  136  which is on the contiguous wall  132 , and the tangent slope of the contiguous wall  132  at the critical point  136  is less than tan 10 ° (0.176). The base point  135  is located at the point where the contiguous wall  132  is connected to the bottom  133 . The straight line L connects a reference point  134  and a base point  135 . An included angle θ is between a straight line L and a horizontal line, and the included angle θ is between 20˜40 degrees, such as 25˜35 degrees. The metal layer  120  has a first width L 1  along the first direction X, and the bottom  133  of the contact hole  131  has a second width L 2  along the first direction X, wherein the first width and the second width satisfy the following equation: 
         [0000]    
       
         
           
             
               2 
               * 
               
                 { 
                 
                   
                     
                       L 
                       2 
                     
                     2 
                   
                   + 
                   
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             p 
                           
                           ) 
                         
                          
                         h 
                       
                       
                         
                           ln 
                            
                           
                             ( 
                             p 
                             ) 
                           
                         
                         · 
                         
                           tan 
                            
                           
                             ( 
                             
                               1.5 
                                
                               θ 
                             
                             ) 
                           
                         
                       
                     
                     · 
                     
                       ln 
                        
                       
                         [ 
                         
                           
                             
                               - 
                               0.176 
                             
                             * 
                             
                               ( 
                               
                                 1 
                                 - 
                                 p 
                               
                               ) 
                             
                           
                           
                             
                               ln 
                                
                               
                                 ( 
                                 p 
                                 ) 
                               
                             
                             · 
                             
                               tan 
                                
                               
                                 ( 
                                 
                                   1.5 
                                    
                                   θ 
                                 
                                 ) 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                 
                 } 
               
             
             = 
             
               L 
               1 
             
           
         
       
     
         [0042]    L 1  is the first width of the metal layer  120  along the first direction X, and L 2  is the second width of the bottom  133  of the contact hole  131  along the first direction X, and p is an adjustable parameter, and (1-p)h is a height of the reference point in a vertical direction, and 0&lt;p≦0.1, such as 0&lt;p≦0.05. By modifying the parameters above, the curvature and the shape of the contiguous wall  132  can be modified. 
         [0043]    In the embodiments above, the contact hole is in the active area (pixel area) A. However, the invention is not limited thereby. The contact hole structure of the embodiment of the invention can also be located in non-active area B. With reference to  FIG. 4 , in one embodiment, the conductive layer  140  in the contact hole  131 ′ is connected to the data line  202 , and the relationship between the profile of the contact hole  131 ′ and the width of the data line  202  can satisfy the above equations. The contact hole  131 ′ is connected to the scan line  201  via the contact hole  131 ″ on the planarization layer  130  and the gate insulation layer  222 . The relationship between the profile of the contact hole  131 ″ and the width of the scan line  201  can satisfy the above equations. In this embodiment, the gate insulation layer  222  is formed between the data line  202  and the scan line  201 . 
         [0044]      FIG. 5  shows a liquid-crystal display  200  of an embodiment of the invention, which comprises an opposite substrate  260 , a liquid-crystal layer  250  and the element 
         [0045]    With reference to Table 1 and  FIG. 6 , in the embodiment of the invention, the width of the metal layer (M 2 )  120  has tolerance of ±1.8. 
         [0000]    
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Sample 1 
                 Sample 2 
                 Sample 3 
                 Sample 4 
                 Sample 5 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Designed 
                 14.54 
                 6.42 
                 8.69 
                 8.12 
                 12.07 
               
               
                 width of the 
               
               
                 metal layer 
               
               
                 (M2) 
               
               
                 Actual width 
                 15.37 
                 7.66 
                 7.41 
                 7.79 
                 11.52 
               
               
                 of the metal 
               
               
                 layer (M2) 
               
               
                 120 
               
               
                 tolerance 
                 0.83 
                 1.24 
                 −1.28 
                 −0.33 
                 −0.55 
               
               
                   
               
             
          
         
       
     
         [0046]    Utilizing the embodiment of the invention, the aperture ratio and the light transmittance (dark state contrast) of the liquid-crystal display are optimized, and the light leakage and the low-contrast problem are prevented. 
         [0047]    Use of ordinal terms such as “first”, “second”, “third”, etc., in the claims to modify a claim element does not by itself connote any priority, precedence, or order of one claim element over another or the temporal order in which acts of a method are performed, but are used merely as labels to distinguish one claim element having a certain name from another element having the same name (but for use of the ordinal term). 
         [0048]    While the invention has been described by way of example and in terms of the preferred embodiments, it is to be understood that the invention is not limited to the disclosed embodiments. On the contrary, it is intended to cover various modifications and similar arrangements (as would be apparent to those skilled in the art). Therefore, the scope of the appended claims should be accorded the broadest interpretation so as to encompass all such modifications and similar arrangements.