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 between 0.087 to 0.364.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application is a Continuation-In-Part of pending U.S. patent application Ser. No. 14/493,173, filed Sep. 22, 2014 and entitled “liquid-crystal display and element substrate thereof, which 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 
     Field of the Invention 
     The present invention relates to a liquid-crystal display, and in particular to a liquid-crystal display having at least one contact hole. 
     Description of the Related Art 
     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 in dark state happens due to the liquid-crystal molecules  2  arranged along the profile of the contact hole  1 , and the contrast ratio of the liquid-crystal display is decreased. 
     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 ratio of the liquid-crystal display. However, this method decreases the aperture ratio and the transmittance in bright state of the liquid-crystal display, and an improved solution is required. 
     BRIEF SUMMARY OF THE INVENTION 
     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 disposed on the metal layer and having a first thickness along a second direction perpendicular to the first direction, wherein the planarization layer comprises a top and a bottom, and the first thickness is a distance between the top and the bottom along the second direction in a pixel region. The planarization layer comprises a contact hole, the contact hole has a contiguous wall and a hole bottom, the hole bottom exposes the metal layer, and the hole 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: 
                 2   *     {         L   2     2     +           (     1   -   p     )     ⁢   h         ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ·     ln   ⁡     [         -   tan     ⁢           ⁢   δ   *     (     1   -   p     )           ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ]           }       -   3.8     ≤     L   1     ≤       2   *     {         L   2     2     +           (     1   -   p     )     ⁢   h         ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ·     ln   ⁡     [         -   tan     ⁢           ⁢   δ   *     (     1   -   p     )           ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ]           }       +   3.8           
wherein L 1  is the first width, and L 2  is the second width, h is the first thickness, δ is an angle between 5 degrees to 20 degrees, θ is an included angle between a straight line and an extension surface of the hole 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 a distance from the reference point to the bottom of the planarization layer along the second direction is 0.95 h. The base point is located at the point where the contiguous wall is connected to the hole bottom, p is an adjustable parameter, and 0&lt;p≦0.1.
 
     Utilizing the embodiment of the invention, the aperture ratio and the contrast ratio of the liquid-crystal display are optimized. 
     A detailed description is given in the following embodiments with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The present invention can be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein: 
         FIG. 1  shows an element substrate of a conventional liquid-crystal display; 
         FIG. 2A  shows cross-section structure of an element substrate of one embodiment of the invention; 
         FIG. 2B  shows cross-section structure of an element substrate of another one embodiment of the invention; 
         FIG. 2C  shows cross-section structure of an element substrate of another one embodiment of the invention; 
         FIG. 3A  shows top-view of the element substrate of the embodiment of the invention utilized in a liquid-crystal display; 
         FIG. 3B  shows top-view of the structure of portion  3 B of  FIG. 3A  in detail; 
         FIG. 3C  shows top-view of the detailed structures of another one embodiment; 
         FIG. 4  shows cross-section structure of the element substrate of another one embodiment of the invention; 
         FIG. 5  shows cross-section structure of a liquid-crystal display of one embodiment of the invention; and 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     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. 
       FIG. 2A  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 L1 along a first direction X. The extending direction of scan lines of the element substrate  100  is parallel to the first direction X. The planarization layer  130  is disposed on the metal layer  120  and has a first thickness h along a second direction Z, the second direction Z is perpendicular to the first direction X, and the second direction Z represent as a normal vector (vertical) of the element substrate  100 . The planarization layer  130  comprises a top and a bottom, and the first thickness h is a distance between the top and the bottom along the second direction Z in a pixel region (PXR), the pixel region locates adjacent to a contact region (CTR) where the contact hole  131  is formed. The planarization layer  130  comprises a contact hole  131 , the contact hole  131  is formed through the planarization layer  130 , the contact hole  131  has a contiguous wall  132  and a hole bottom  133 , the hole bottom  133  exposes the metal layer  120 , and the hole bottom  133  of the contact hole  131  has a second width L2 along the first direction X. 
     The applicant has discovered that the liquid-crystal molecules are arranged along the contiguous wall  132 , and the light transmittance 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 in dark state is acceptable, and the contrast ratio 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 (transmittance) and the contrast ratio are optimized. 
     With reference to  FIG. 2A , 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 contrast ratio are optimized: 
                 2   *     {         L   2     2     +         0.9   ⁢           ⁢   5   ⁢   h         ln   ⁡     (   0.5   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ·     ln   ⁡     [         -   tan     ⁢           ⁢     δ   ·   0.95           ln   ⁡     (   0.05   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ]           }       -   3.8     ≤     L   1     ≤       2   *     {         L   2     2     +         0.95   ⁢   h         ln   ⁡     (   0.05   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ·     ln   ⁡     [         -   tan     ⁢           ⁢     δ   ·   0.95           ln   ⁡     (   0.05   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ]           }       +   3.8           
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 hole bottom  133  of the contact hole  131  along the first direction X, h is a first thickness (the first thickness is a distance between the top of the planarization layer  130  and the bottom of the planarization layer  130  along the second direction Z in a pixel region), δ is an angle between 5 degrees to 20 degrees, θ is an included angle between a straight line L and an extension surface of the hole 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 a distance from the reference point  134  to bottom of the planarization layer along the second direction is 0.95h. The base point  135  is located at the point where the contiguous wall  132  is connected to the hole bottom  133 , and ±3.8 is the tolerance. By modifying the parameters above, the curvature and the shape of the contiguous wall  132  can be modified.
 
     The tangent slope of a particular point on a top curvature of the polarization layer  130  is tans, and the angle δ is an included angle (acute angle) between a tangent line of the particular point and a horizontal line passes through the particular point (the horizontal line is perpendicular to the second direction Z). The angle δ of particular point corresponding to the pixel region (PXR) is between 0 to 2 degrees. The angle δ of particular point corresponding to the contact region (CTR) is between 2 degrees to 90 degrees. The critical point  136  is one of a set formed by a plurality of particular points of the contact region. In the embodiment above, in the contact region, the angle δ is an angle between 5 degrees to 20 degrees to make optimization between the aperture ratio (transmittance) and contrast ratio of the liquid crystal display. In one embodiment, to achieve an improved aperture ratio (transmittance), the angle δ is smaller than 10 degrees, and the angle δ is greater than or equal to 5 degrees (5 degrees≦δ&lt;10 degrees). In another one embodiment, to achieve an improved contrast ratio (low light leakage in dark state), the angle δ is greater than 10 degrees, and the angle δ is smaller than or equal to 20 degrees (10 degrees&lt;δ≦20 degrees). 
     With reference to  FIG. 2A , the derivative of the curve equation is presented in the following description. 
     First, curve fitting (assuming), assuming a curve equation of the contiguous wall of the contact hole is:
 
 y=f ( x )=− A ′exp(− x )   (1)
 
     In equation (1), only asymptotes of the contiguous wall are defined, and the equation (1) must be regulated relative to the first direction X (X axis) and a third direction Y (Y axis), wherein the first direction X, the second direction Z, and the third direction Y are perpendicular to each other. 
     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: 
     
       
         
           
             
               
                 
                   
                     
                       f 
                       ⁡ 
                       
                         ( 
                         
                           R 
                           ′ 
                         
                         ) 
                       
                     
                     = 
                     
                       
                         - 
                         ph 
                       
                       = 
                       
                         
                           
                             
                               - 
                               h 
                             
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             
                               exp 
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     - 
                                     
                                       R 
                                       ′ 
                                     
                                   
                                   α 
                                 
                                 ) 
                               
                             
                           
                           ⁢ 
                           
                             
 
                           
                           ⇒ 
                           α 
                         
                         = 
                         
                           
                             - 
                             
                               R 
                               ′ 
                             
                           
                           
                             ln 
                             ⁡ 
                             
                               ( 
                               p 
                               ) 
                             
                           
                         
                       
                     
                   
                   ; 
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
             
               
                 
                   
                     p 
                     &gt; 
                     0 
                   
                   , 
                   
                     h 
                     &gt; 
                     0 
                   
                   , 
                   
                     
                       R 
                       ′ 
                     
                     &gt; 
                     0 
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
         
         
           
             Correction parameter α is achieved. 
           
         
       
    
     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 θ, then: 
     
       
         
           
             
               
                 
                   
                     tan 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     θ 
                   
                   = 
                   
                     
                       
                         
                           
                             ( 
                             
                               1 
                               - 
                               p 
                             
                             ) 
                           
                           ⁢ 
                           h 
                         
                         
                           R 
                           ′ 
                         
                       
                       ⁢ 
                       
                         
 
                       
                       ⇒ 
                       
                         R 
                         ′ 
                       
                     
                     = 
                     
                       
                         
                           ( 
                           
                             1 
                             - 
                             p 
                           
                           ) 
                         
                         ⁢ 
                         h 
                       
                       
                         tan 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
           
         
       
         
         
           
             Material property θ is brought in. 
           
         
       
    
     Next, a distance between the reference point and the bottom of the planarization layer along the second direction Z is 0.95h. By combining equations of equation (2) and equation (3), we get: 
     
       
         
           
             
               
                 
                   α 
                   = 
                   
                     
                       
                         - 
                         
                           R 
                           ′ 
                         
                       
                       
                         ln 
                         ⁡ 
                         
                           ( 
                           0.05 
                           ) 
                         
                       
                     
                     = 
                     
                       
                         
                           - 
                           0.95 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         h 
                       
                       
                         
                           
                             ln 
                             ⁡ 
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           tan 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         θ 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
         
         
           
             Correction parameter α is achieved. 
           
         
       
    
     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 is about 1.5θ. Therefore, by revising the curve equation (angle revising) further, we get: 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           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 
                   ) 
                 
               
             
           
         
       
     
     Curve equation of the contact hole is achieved. 
     Next, R=R 0 +R′, by bringing this equation into the above equation, we get: 
     
       
         
           
             
               
                 
                   
                     
                       ∵ 
                       
                         R 
                         ′ 
                       
                     
                     = 
                     
                       R 
                       - 
                       
                         
                           R 
                           0 
                         
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         … 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         
                           ( 
                           shiftting 
                           ) 
                         
                       
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         
                           
                             ⇒ 
                             
                               f 
                               ⁡ 
                               
                                 ( 
                                 
                                   R 
                                   ′ 
                                 
                                 ) 
                               
                             
                           
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 - 
                                 h 
                               
                               · 
                               exp 
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   - 
                                   
                                     ( 
                                     
                                       R 
                                       - 
                                       
                                         R 
                                         0 
                                       
                                     
                                     ) 
                                   
                                 
                                 / 
                                 α 
                               
                               } 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                           ⁢ 
                           
                             
                               
                                 - 
                                 h 
                               
                               · 
                               exp 
                             
                             ⁢ 
                             
                               { 
                               
                                 
                                   ( 
                                   
                                     R 
                                     - 
                                     
                                       R 
                                       0 
                                     
                                   
                                   ) 
                                 
                                 · 
                                 
                                   
                                     
                                       ln 
                                       ⁡ 
                                       
                                         ( 
                                         0.05 
                                         ) 
                                       
                                     
                                     · 
                                     
                                       tan 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           1.5 
                                           ⁢ 
                                           θ 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     0.95 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     h 
                                   
                                 
                               
                               } 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
     
     Actual curve equation of the contact hole is achieved. 
     Next, as mentioned above, at the location where the tangent slope of the particular point of the contiguous wall  132  is tan δ, the light leakage is acceptable, and the contrast ratio of the liquid-crystal display is qualified, and the aperture ratio and the contrast ratio are optimized. The equation of half of the second width of the metal layer along the first direction is: 
     
       
         
           
             
               
                 
                   
                       
                   
                   ⁢ 
                   
                     
                       
                         ∂ 
                         
                           f 
                           ⁡ 
                           
                             ( 
                             
                               R 
                               ′ 
                             
                             ) 
                           
                         
                       
                       
                         ∂ 
                         
                           R 
                           ′ 
                         
                       
                     
                     = 
                     
                       
                         tan 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         δ 
                       
                       = 
                       
                         
                           
                             
                               ∂ 
                               
                                 ∂ 
                                 
                                   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 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                         
                         = 
                         
                           
                             
                               tan 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               δ 
                             
                             ⁢ 
                             
                               
 
                             
                             ⁢ 
                             
                                 
                             
                             ⇒ 
                             
                               exp 
                               ⁡ 
                               
                                 [ 
                                 
                                   
                                     R 
                                     ′ 
                                   
                                   · 
                                   
                                     
                                       
                                         ln 
                                         ⁡ 
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1.5 
                                             ⁢ 
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                     
                                       0.95 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       h 
                                     
                                   
                                 
                                 ] 
                               
                             
                           
                           = 
                           
                             
                               
                                 
                                   
                                     - 
                                     tan 
                                   
                                   ⁢ 
                                   
                                       
                                   
                                   ⁢ 
                                   
                                     δ 
                                     · 
                                     0.95 
                                   
                                 
                                 
                                   
                                     ln 
                                     ⁡ 
                                     
                                       ( 
                                       0.05 
                                       ) 
                                     
                                   
                                   · 
                                   
                                     tan 
                                     ⁡ 
                                     
                                       ( 
                                       
                                         1.5 
                                         ⁢ 
                                         θ 
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ⁢ 
                               
                                 
 
                               
                               ⁢ 
                               
                                   
                               
                               ⇒ 
                               
                                 
                                   R 
                                   ′ 
                                 
                                 · 
                                 
                                   
                                     
                                       ln 
                                       ⁡ 
                                       
                                         ( 
                                         0.05 
                                         ) 
                                       
                                     
                                     · 
                                     
                                       tan 
                                       ⁡ 
                                       
                                         ( 
                                         
                                           1.5 
                                           ⁢ 
                                           θ 
                                         
                                         ) 
                                       
                                     
                                   
                                   
                                     0.95 
                                     ⁢ 
                                     
                                         
                                     
                                     ⁢ 
                                     h 
                                   
                                 
                               
                             
                             = 
                             
                               
                                 
                                   ln 
                                   ⁡ 
                                   
                                     [ 
                                     
                                       
                                         
                                           - 
                                           tan 
                                         
                                         ⁢ 
                                         
                                             
                                         
                                         ⁢ 
                                         
                                           δ 
                                           · 
                                           0.95 
                                         
                                       
                                       
                                         
                                           ln 
                                           ⁡ 
                                           
                                             ( 
                                             0.05 
                                             ) 
                                           
                                         
                                         · 
                                         
                                           tan 
                                           ⁡ 
                                           
                                             ( 
                                             
                                               1.5 
                                               ⁢ 
                                               θ 
                                             
                                             ) 
                                           
                                         
                                       
                                     
                                     ] 
                                   
                                 
                                 ⁢ 
                                 
                                   
 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⇒ 
                                 
                                   
                                     R 
                                     ′ 
                                   
                                   · 
                                   
                                     
                                       0.95 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       h 
                                     
                                     
                                       
                                         ln 
                                         ⁡ 
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1.5 
                                             ⁢ 
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   · 
                                   
                                     ln 
                                     ⁡ 
                                     
                                       [ 
                                       
                                         
                                           
                                             - 
                                             tan 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             δ 
                                             · 
                                             0.95 
                                           
                                         
                                         
                                           
                                             ln 
                                             ⁡ 
                                             
                                               ( 
                                               0.05 
                                               ) 
                                             
                                           
                                           · 
                                           
                                             tan 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 1.5 
                                                 ⁢ 
                                                 θ 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                                 ⁢ 
                                 
                                   
 
                                 
                                 ⁢ 
                                 
                                     
                                 
                                 ⇒ 
                                 R 
                               
                               = 
                               
                                 
                                   R 
                                   0 
                                 
                                 + 
                                 
                                   
                                     
                                       0.95 
                                       ⁢ 
                                       
                                           
                                       
                                       ⁢ 
                                       h 
                                     
                                     
                                       
                                         ln 
                                         ⁡ 
                                         
                                           ( 
                                           0.05 
                                           ) 
                                         
                                       
                                       · 
                                       
                                         tan 
                                         ⁡ 
                                         
                                           ( 
                                           
                                             1.5 
                                             ⁢ 
                                             θ 
                                           
                                           ) 
                                         
                                       
                                     
                                   
                                   · 
                                   
                                     ln 
                                     ⁡ 
                                     
                                       [ 
                                       
                                         
                                           
                                             - 
                                             tan 
                                           
                                           ⁢ 
                                           
                                               
                                           
                                           ⁢ 
                                           
                                             δ 
                                             · 
                                             0.95 
                                           
                                         
                                         
                                           
                                             ln 
                                             ⁡ 
                                             
                                               ( 
                                               0.05 
                                               ) 
                                             
                                           
                                           · 
                                           
                                             tan 
                                             ⁡ 
                                             
                                               ( 
                                               
                                                 1.5 
                                                 ⁢ 
                                                 θ 
                                               
                                               ) 
                                             
                                           
                                         
                                       
                                       ] 
                                     
                                   
                                 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   7 
                   ) 
                 
               
             
           
         
       
     
     Considering that ±3.8 is acceptable manufacturing tolerance, when the first width and the second width satisfy the following equation, the aperture ratio and the contrast ratio are optimized: 
     
       
         
           
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.9 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           5 
                           ⁢ 
                           h 
                         
                         
                           
                             ln 
                             ⁡ 
                             
                               ( 
                               0.5 
                               ) 
                             
                           
                           · 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 1.5 
                                 ⁢ 
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 - 
                                 tan 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 δ 
                                 · 
                                 0.95 
                               
                             
                             
                               
                                 ln 
                                 ⁡ 
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1.5 
                                     ⁢ 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               - 
               3.8 
             
             ≤ 
             
               L 
               1 
             
             ≤ 
             
               
                 2 
                 * 
                 
                   { 
                   
                     
                       
                         L 
                         2 
                       
                       2 
                     
                     + 
                     
                       
                         
                           0.95 
                           ⁢ 
                           h 
                         
                         
                           
                             ln 
                             ⁡ 
                             
                               ( 
                               0.05 
                               ) 
                             
                           
                           · 
                           
                             tan 
                             ⁡ 
                             
                               ( 
                               
                                 1.5 
                                 ⁢ 
                                 θ 
                               
                               ) 
                             
                           
                         
                       
                       · 
                       
                         ln 
                         ⁡ 
                         
                           [ 
                           
                             
                               
                                 - 
                                 tan 
                               
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               
                                 δ 
                                 · 
                                 0.95 
                               
                             
                             
                               
                                 ln 
                                 ⁡ 
                                 
                                   ( 
                                   0.05 
                                   ) 
                                 
                               
                               · 
                               
                                 tan 
                                 ⁡ 
                                 
                                   ( 
                                   
                                     1.5 
                                     ⁢ 
                                     θ 
                                   
                                   ) 
                                 
                               
                             
                           
                           ] 
                         
                       
                     
                   
                   } 
                 
               
               + 
               3.8 
             
           
         
       
     
     In one embodiment, to achieve aperture ratio and contrast ratio balanced, the angle δ could be equal to 10 degrees. In another one embodiment, to achieve an improved aperture ratio (transmittance), the angle δ is smaller than 10 degrees, and the angle δ is greater than or equal to 5 degrees (5 degrees≦δ&lt;10 degrees). In another one embodiment, to achieve an improved contrast ratio (low light leakage in dark state), the angle δ is greater than 10 degrees, and the angle δ is smaller than or equal to 20 degrees (10 degrees&lt;δ≦20 degrees) 
     With reference to  FIG. 2A , the element substrate  100  further comprises a first conductive layer  140  disposed on the planarization layer  130  in the contact region, wherein the first conductive layer  140  is electrically connected to the metal layer  120  via the contact hole  131 . The first conductive layer  140  is made of transparent material or metal. In one embodiment, a second conductive layer  141  is disposed on the planarization layer  130  in the pixel region. The second conductive layer  141  can be the same with or different from the first conductive layer  140 . 
       FIG. 2B  shows another element substrate of an embodiment of the invention. With reference to  FIG. 2B , the metal layer  120  is a source electrode or a drain electrode of a driving element (TFT). The metal layer can contact with a semiconductor layer made of polycrystalline silicon, noncrystalline silicon or metal oxide. In one embodiment, the element substrate  100  further comprises a first insulation layer  138 , a second insulation layer  139  and a third insulation layer  170 . The first insulation layer  138  is located between the metal layer  120  and the substrate  110 . The first insulation layer  138  can be made of silicon oxide, silicon nitride, alumina nitride, or other transparent materials. The second insulation layer  139  is located between the metal layer  120  and the planarization layer  130 , wherein the contact hole  131  passing through the planarization layer  130  and the second insulation layer  139  to expose the metal layer  120 . The material of second insulation layer  139  could be the same with the first insulation layer  138 . The third insulation layer  170  is located between the first conductive layer  140  and the planarization layer  130 . The material of third insulation layer  170  could be the same with the first insulation layer  138 .  FIG. 2C  shows another element substrate of an embodiment of the invention, wherein the third insulation layer  170  is located between the second conductive layer  141  and the planarization layer  130 . 
       FIG. 3A  shows the element substrate of the embodiment of the invention utilized in a liquid-crystal display  200 , which comprises an active area A and an peripheral 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  (along the first direction X), data lines  202  (along the third direction Y), a semiconductor layer  203 , source electrodes  240 , a contact hole  231 , a hole 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  could be the source electrodes  240 , the drain electrodes  204 , the scan lines  201  or the signal lines  202 . The contact hole  231  defines a contact region, and the pixel region is adjacent to the contact region.  FIG. 3C  shows the detailed structures of another one embodiment, wherein slits  206  of the pixel electrodes  210  extends along the third direction Y. 
     With reference to  FIG. 2A , in another one embodiment, the metal  120  comprises a first edge  121 , 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 tan δ (5 degrees≦δ≦20 degrees). The base point  135  is located at the point where the contiguous wall  132  is connected to the hole 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. The metal layer  120  has a first width L1 along the first direction X, and the hole bottom  133  of the contact hole  131  has a second width L2 along the first direction X, wherein the first width and the second width satisfy the following equation: 
               2   *     {         L   2     2     +           (     1   -   p     )     ⁢   h         ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ·     ln   ⁡     [         -   tan     ⁢           ⁢   δ   *     (     1   -   p     )           ln   ⁡     (   p   )       ·     tan   ⁡     (     1.5   ⁢   θ     )           ]           }       =     L   1           
L1 is the first width of the metal layer  120  along the first direction X, and L2 is the second width of the hole bottom  133  of the contact hole  131  along the first direction X, and p is an adjustable parameter, and 0&lt;p≦0.1. By modifying the parameters above, the curvature and the shape of the contiguous wall  132  can be modified.
 
     In the embodiments above, the contact hole is in the active area A. However, the invention is not limited thereby. The contact hole structure of the embodiment of the invention can also be located in peripheral area B. With reference to  FIG. 4 , in one embodiment, the first conductive layer  140  is connected to the data line  202  via the contact hole  131 ′ of the planarization layer  130 , 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 first conductive layer  140  is connected to the scan line  201  via the contact hole  131 ″ of 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 . 
       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 , a sealant structure and the element substrate  100 . The liquid-crystal layer  250  is disposed between the element substrate  100  and the opposite substrate  260  and surrounded by the sealant structure. The opposite substrate  260  may comprises color filter layer. The element substrate  100  could be connected with drivers or printed circuit board. 
     With reference to Table 1, in the embodiment of the invention, the width of the metal layer (M 2 )  120  has tolerance of ±3.8. 
     
       
         
               
               
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 Sample 1 
                 Sample 2 
                 Sample 3 
                 Sample 4 
                 Sample 5 
                 Sample 6 
                 Sample 7 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                 Designed 
                 14.54 
                 6.42 
                 8.69 
                 8.12 
                 12.07 
                 23.56 
                 31.37 
               
               
                 width of 
               
               
                 the metal 
               
               
                 layer 
               
               
                 (M2) 
               
               
                 Actual 
                 15.37 
                 7.66 
                 7.41 
                 7.79 
                 11.52 
                 19.84 
                 34.93 
               
               
                 width of 
               
               
                 the metal 
               
               
                 layer 
               
               
                 (M2) 120 
               
               
                 tolerance 
                 0.83 
                 1.24 
                 −1.28 
                 −0.33 
                 −0.55 
                 −3.72 
                 −3.56 
               
               
                   
               
             
          
         
       
     
     Utilizing the embodiment of the invention, the aperture ratio and the contrast ratio of the liquid-crystal display are optimized, and the light leakage and the low-contrast ratio problem are prevented. 
     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). 
     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.