Patent Publication Number: US-2023154956-A1

Title: Image sensor

Description:
CROSS - REFERENCE TO RELATED APPLICATION 
     This application claims priority to U.S. Provisional Application Serial No. 63/279,882, filed on Nov. 16, 2021, which is herein incorporated by reference in its entirety. 
    
    
     BACKGROUND 
     Field of Invention 
     The present invention relates to an image sensor. 
     Description of Related Art 
     An image sensor can detect and convey information used to make an image. Image sensors are used in various imaging devices such as digital cameras, optical mouse devices, medical imaging equipment, thermal imaging devices, radar, sonar, and so on. 
     A traditional image sensor may include a color filter, a micro lens, and multiple photo diodes. However, when three is a shift between the micro lens and the photo diodes, the energy received by the photo diodes will be uneven. As a result, performance of the photo diodes is degraded. Therefore, it is still a development direction for the industry to provide an image sensor which can solve the problem mentioned above. 
     SUMMARY 
     One aspect of the invention provides an image sensor. 
     In some embodiments, the image sensor includes a first pixel array. The first pixel array includes multiple photo diodes and a polyhedron structure. The polyhedron structure is located above the photo diodes. The polyhedron structure is configured to divide an incident light into multiple light beams, and each of the light beams is respectively focused in each of the photo diodes. The polyhedron structure includes a bottom facet, a top facet, and at least one side facet. The bottom facet is located between the side facet and the photo diodes, and an orthogonal projection of the polyhedron structure overlaps with the photo diodes. 
     In the aforementioned embodiment, the polyhedron structure is configured to divide an incident light into multiple light beams towards the photo diodes. In addition, a number of the light beam can be determined by a number of the side facets of the polyhedron structure. A position of the focus of the light beam can be determined by the area of the top facet of the polyhedron structure, the height of the polyhedron, or the refractive index of the polyhedron structure. As such, focuses of the light beams are positioned more correlated with positions of photo diodes. Therefore, performance of the photo diodes can be improved. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The invention can be more fully understood by reading the following detailed description of the embodiment, with reference made to the accompanying drawings as follows: 
         FIG.  1    is a top view of an image sensor  10  according to one embodiment of the present embodiment. 
         FIG.  2    is a three-dimensional view of a first pixel array  100  of the image sensor  10  in  FIG.  1   . 
         FIG.  3    is a schematic of optical path of an incident light traveling through a polyhedron structure. 
         FIGS.  4 A to  4 E  are schematics of various polyhedron structures according to some embodiments of the present disclosure. 
         FIGS.  5 A to  5 E  are top views of the polyhedron structures shown in  FIGS.  4 A to  4 E . 
         FIGS.  6 A to  6 D  are schematics of various polyhedron structures according to some embodiments of the present disclosure. 
         FIGS.  7 A to  7 D  are illuminance diagram of the photo diodes in combination with the polyhedron structures shown in  FIGS.  6 A to  6 D . 
         FIG.  8    is a side view of a first pixel array according to one embodiment of the present disclosure. 
         FIGS.  9 A to  9 D  are top views of image sensors according to some embodiments of the present disclosure. 
         FIG.  10 A  is a schematic of a polyhedron structure. 
         FIG.  10 B  and  FIG.  10 C  are top views of image sensors according to some embodiments of the present disclosure. 
         FIGS.  11 Ato  11  B ,  FIGS.  12 A to  12 C , and  FIGS.  13 A to  13 C  are top views of image sensors according to some embodiments of the present disclosure. 
         FIG.  14 A  is a side view of an image sensor  10   o  according to one embodiment of the present disclosure. 
         FIG.  14 B  is a top view of the image sensor in  FIG.  14 A . 
         FIG.  14 C  and  FIG.  14 D  are top views of the image sensors according to some embodiments of the present disclosure. 
         FIGS.  15 A to  15 E  are cross-sectional views of image sensors according to some embodiments of the present disclosure. 
         FIGS.  16 A to  16 E  are top views of color arrangement of the color filters of the image sensors according to some embodiments of the present disclosure. 
         FIGS.  17 A to  17 D  are top views of color arrangement of the color filters of the image sensors according to some embodiments of the present disclosure. 
         FIG.  18    is an electromagnetic field simulation result. 
         FIG.  19    is a schematic of a pixel array  300  according to one embodiment of the present disclosure. 
         FIG.  20 A  and  FIG.  20 B  are schematics of light distribution on the polyhedron structure according to some embodiment of the present disclosure. 
         FIG.  21 A  and  FIG.  21 B  are top views of an image sensor according to one embodiment of the present disclosure. 
         FIG.  22    is a schematic of a pixel array according to one embodiment of the present embodiment. 
         FIG.  23    is a plot of relation between focusing separation distance and a height of polyhedron structure. 
         FIGS.  24 A to  24 D  are illuminance diagrams of the photo diodes with various height of the polyhedron structure. 
         FIGS.  25 A to  25 B ,  FIGS.  26 A to  26 B ,  FIGS.  27 A to  27 B ,  FIGS.  28 A to  28 C ,  FIGS.  29 A to  29 B ,  FIGS.  30 A to  30 B ,  FIGS.  31 A to  31 E , and  FIGS.  32 A to  32 D  are top views of image sensors according to some embodiments of the present disclosure. 
         FIG.  33 A  is a partial top view of an image sensor according to one embodiment of the present disclosure. 
         FIG.  33 B  is a cross-sectional view taken along line  33 B- 33 B in  FIG.  33 A . 
         FIG.  33 C  and  FIG.  33 D  are top view of image sensors according to some embodiments of the present disclosure. 
         FIG.  34    is a schematic of optical path when an incident light traveling through the polyhedron structure. 
         FIG.  35 A  is a partial top view of an image sensor according to one embodiment of the present disclosure. 
         FIG.  35 B  and  FIG.  35 C  are top view of image sensors according to some embodiments of the present disclosure. 
         FIGS.  36 A to  36 C  are cross-sectional view of pixel arrays according to some embodiments of the present disclosure. 
         FIG.  37    is an electromagnetic field simulation result. 
     
    
    
     DETAILED DESCRIPTION 
     Reference will now be made in detail to the present embodiments of the invention, examples of which are illustrated in the accompanying drawings. Wherever possible, the same reference numbers are used in the drawings and the description to refer to the same or like parts. 
       FIG.  1    is a top view of an image sensor  10  according to one embodiment of the present embodiment.  FIG.  2    is a three-dimensional view of a first pixel array  100  of the image sensor  10  in  FIG.  1   . Reference is made to  FIG.  1    and  FIG.  2   . The image sensor  10  includes four first pixel arrays  100 . The first pixel array  100  is a multi photo diode structure applied in an image sensor such as CMOS image sensor (CIS). The first pixel array  100  includes a polyhedron structure  110 , a photoelectric conversion layer  120 , a color filter  130 , and an under layer  140 . The photoelectric conversion layer  120  includes multiple photo diodes  122 . The polyhedron structure  110  is located above the photoelectric conversion layer  120 , the under layer  140 , and the color filter  130 . The color filter  130  is located between the under layer  140  and the photoelectric conversion layer  120 . The under layer  140  is located between the blue color filter layer  130  and the polyhedron structure  110 . 
     The polyhedron structure  110  includes a bottom facet  112 , a top facet  114 , and at least one side facet  116 . An area of the bottom facet  112  is greater than an area of the top facet  114 , and a number of the side facets  116  is greater than or equal to three. The bottom facet  112  is located between the side facets  116  and the under layer  140 . An orthogonal projection of the polyhedron structure  110  overlaps with more than or equal to two photo diodes  122 . In the present embodiments, the polyhedron structure  110  has four side facets  116 . In other words, the polyhedron structure  110  is a hexahedron. The polyhedron structure  110  is transparent, and the material of the polyhedron structure  110  includes photoresist, plastic, organic material, inorganic material, or other suitable materials. 
     In the present embodiment, the first pixel array  100  has four pixels  12 , and each of the pixels  12  has one photo diode  122 . Therefore, the orthogonal projection of the polyhedron structure  110  overlaps with four photo diodes  122 . That is, the first pixel array  100  is a quad photo diode (QPD). In some embodiments, the under layer  140  and the filter layer  130  can be omitted, or other structures can be disposed between the polyhedron structure  110  and the photoelectric conversion layer  120 . 
       FIG.  3    is a schematic of optical path of an incident light L 1  traveling through a polyhedron structure  110 . The polyhedron structure  110  is configured to divide an incident light L 1  into multiple light beams. Each of the light beams is respectively focused in each of the photo diodes. The number of the light beam is determined by a number of the side facets  116  so as to improve performance of the photo diodes  122 . For example, the polyhedron structure  110  can divide the incident light L 1  into five light beams each passes through the side facets  116  and the top facet  114 . Only three light beams are demonstrated in  FIG.  3   . A light beam L 2  and a light beam L 3  respectively travel toward the photo diodes  122 , and a portion of the incident light L 1  travels downward. 
     A position of the focus of the light beam is determined by the area of the top facet  114 . For example, if a height H1 of the polyhedron structure  110  is fixed, the inclined level of the side facets  116  becomes greater when the area of the top facet  114  increases. As a result, focal lengths of the light beams L 2 , L 3  are shorter. Therefore, the direction of the light beams L 2 , L 3  can be adjusted by controlling the area of the top facet  114 . As such, focuses of the light beams L 2 , L 3  are positioned more correlated with positions of photo diodes. 
       FIGS.  4 A to  4 E  are schematics of various polyhedron structures according to some embodiments of the present disclosure.  FIGS.  5 A to  5 E  are top views of the polyhedron structures shown in  FIGS.  4 A to  4 E . As shown in  FIG.  4 A  and  FIG.  5 A , the polyhedron structure  110   a  is a tetrahedron, and the polyhedron structure  110   a  has a triangular pyramid shape. The polyhedron structure  110   a  includes three vertexes  111   a  formed by the bottom facet  112   a  and the side facets  116   a  and a vertex  113   a  above the side facets  116   a . 
     As shown in  FIG.  4 B  and  FIG.  5 B , the polyhedron structure  110   b  is a pentahedron, and the polyhedron structure  110   a  has a quadrangular pyramid shape. The polyhedron structure  110   b  includes four vertexes  111   b  formed by the bottom facet  112   b  and the side facets  116   b  and a vertex  113   b  formed by the side facets  116   b . 
     As shown in  FIG.  4 C  and  FIG.  5 C , the polyhedron structure  110   c  is a pentahedron, and the polyhedron structure  110   c  has a triangular column shape. The polyhedron structure  110   c  includes three vertexes  111   c  formed by the bottom facet  112   c  and the side facets  116   c  and three vertexes  111   c  formed by the top facet  114   c  and the side facets  116   c . As shown in  FIG.  4 D  and  FIG.  5 D , the polyhedron structure  110   d  is a pentahedron, and the polyhedron structure  110   d  has a roof shape. The polyhedron structure  110   d  includes four vertexes  111   d  formed by the bottom facet  112   d  and the side facets  116   d  and two vertexes formed by side facets  116   d . As shown in  FIGS.  4 E and  5 E , the polyhedron structure  110   e  is a hexahedron, and the polyhedron structure  110   e  has a pentagonal pyramid shape. The polyhedron structure  110   e  includes five vertexes  111   e  formed by the bottom facet  112   e  and the side facets  116   e  and a vertex  113   e  formed by the side facets  116   e . 
       FIGS.  6 A to  6 D  are schematics of various polyhedron structures according to some embodiments of the present disclosure.  FIGS.  7 A to  7 D  are illuminance diagram of the photo diodes in combination with the polyhedron structures shown in  FIGS.  6 A to  6 D . As shown in  FIG.  6 A  and  FIG.  7 A , the polyhedron structure  110   f  has eight side facets  116   f , and therefore an incident light is divided into eight light beams. As shown in  FIG.  6 B  and  FIG.  7 B , the polyhedron structure  110   g  has eight side facets  116   g  and a top facet  114   g , and therefore an incident light is divided into nine light beams. As shown in  FIG.  6 C  and  FIG.  7 C , the polyhedron structure  110   h  has a corn shape (i.e., infinite number of side facets), and therefore an incident light is reshaped as a ring-shaped light. As shown in  FIG.  6 D  and  FIG.  7 D , the polyhedron structure  110   i  has a corn shape with a top facet  116   i , and therefore an incident light is reshaped as a ring-shaped light and a light beam at the center of the ring-shaped light. 
     The polyhedron structure of the present discloser is not limited to those embodiments described above in  FIGS.  4 A to  44 E  and  FIGS.  6 A to  6 D . Suitable shapes of the polyhedron structures can be used based on the arrangement of pixels so as improve performance of the photo diodes. As such, focuses of the light beams are positioned more correlated with positions of photo diodes. 
     Reference is made to  FIG.  1   . A refractive index of the polyhedron structure  110  is greater than or equal to 1.1 and is smaller than a refractive index of the photo diodes  122 . Specifically, the refractive index of the photo diodes  122  is greater than a refractive index of the color filter  130 , and the refractive index of the color filter  130  is greater than a refractive index of the under layer  140 . The refractive index of the under layer  140  is greater than or equal to the refractive index of the polyhedron structure  110 . With such configuration, light transmission efficiency and performance of the photo diodes  122  can be improved. 
       FIG.  8    is a side view of a first pixel array  100   a  according to one embodiment of the present disclosure. The first pixel array  100   a  is similar to the first pixel array  100  shown in  FIG.  2   , and the difference is that the first pixel array  100   a  further includes an antireflection layer  150  coated on the polyhedron structure  110 . In the present embodiment, a refractive index of the antireflection layer  150  is greater than 1.1 and is smaller than a refractive index of the polyhedron structure  110 . With such configuration, light transmission efficiency and performance of the photo diodes  122  can be further improved. 
       FIGS.  9 A to  9 D  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  9 A , the image sensor  10   a  has sixty-four photo diodes  122  (i.e., sixty-four pixels) and sixteen polyhedron structures  110 . The polyhedron structures  110  are arranged as a 4x4 array. Each of the polyhedron structures  110  overlaps with four photo diodes  122  which are arranged as a 2x2 array. As shown in  FIG.  9 B , the image sensor  10   b  has eighty-one photo diodes  122  and nine polyhedron structures  110 . The polyhedron structures  110  are arranged as a 3x3 array. Each of the polyhedron structures  110  is overlapped with nine photo diodes  122  which are arranged as a 2x2 array. As shown in  FIG.  9 C , the image sensor  10   c  has sixty-four photo diodes  122  and four polyhedron structures  110 . The polyhedron structures  110  are arranged as a 2x2 array. Each of the polyhedron structures  110  overlaps with sixteen photo diodes  122  which are arranged as a 4x4 array. As shown in  FIG.  9 D , the image sensor  10   d  has one hundred photo diodes  122  and four polyhedron structures  110 . The polyhedron structures  110  are arranged as a 2x2 array. Each of the polyhedron structures  110  overlaps with twenty-five photo diodes  122  which are arranged as a 5x5 array. The present disclosure is not limited to those configurations shown in  FIGS.  9 A to  9 D . 
       FIG.  10 A  is a schematic of a polyhedron structure  110   j .  FIG.  10 B  and  FIG.  10 C  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  10 A  and  FIG.  10 B , the image sensor  10   e  includes nine third pixel arrays  100   c . Each of the third pixel arrays  100   c  includes one polyhedron structures  110   j  and nine photo diodes  122  (i.e., nine pixels). Each of the polyhedron structures  110   j  has eight side facets  116 , a square bottom facet  112  and a circular top facet  114 . Each of the polyhedron structures  110   j  overlaps with nine photo diodes  122  arranged as a 3x3 array. Therefore, a sum of a number of the side facets  116  and a number of the top facet  114  of the polyhedron structure  110   j  is equal to a number of the photo diodes  122 . 
     As shown in  FIG.  10 C , the image sensor  10   f  has four fourth pixel arrays  100   d . Each of the fourth pixel arrays  100   d  includes one polyhedron structure  110   k  and sixteen photo diodes  122 . The polyhedron structure  110   k  is similar to polyhedron structure  110   j , and the difference is that the polyhedron structure  110   k  has sixteen side facets  116 . Each of the polyhedron structures  110   k  overlaps with sixteen photo diodes  122  arranged as a 4x4 array. Therefore, a sum of a number of the side facets  116  and a number of the top facet  114  of the polyhedron structure  110   k  equals to the number of the photo diodes  122 . 
     In the embodiments shown in  FIG.  10 B  and  FIG.  10 C , the polyhedron structure  110   j  and the polyhedron structure  110   k  are prism. The energy of an incident light can be distributed more uniformly to the one or more pixels underlying the top fact  114  and the pixels underlying the side facets  116 . 
       FIG.  11 A  and  FIG.  11 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  11 A , the image sensor  10   g  includes fourteen first pixel arrays  100 A and one second pixel array  100 B. The first pixel arrays  100 A is the same as the first pixel array  100  described in  FIG.  2   . The second pixel array  100 B has eight photo diodes  122  arranged as a 4x2 array, and there is no polyhedron structure  110  located above the photo diodes  122  of the second pixel array  100 B. As shown in  FIG.  11 B , the image sensor  10   h  includes twelve first pixel arrays  100 A and one second pixel array  100 B. The second pixel array  100 B includes sixteen photo diodes  122  arranged as a 4x4 array, and there is no polyhedron structures  110  located above the photo diodes  122  of the second pixel array  100 B. The configurations of the image sensor  10   g  and the image sensor  10   h  can be utilized for specific functions such as auto focus function. In some other embodiments, the pixel arrays which have no polyhedron structures can be randomly arranged in the image sensor. 
       FIGS.  12 A to  12 C  are top view of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  12 A , the image sensor  10   i  includes fourteen first pixel array  100 A and one second pixel array  100 B. Each of the first pixel arrays  100 A includes a polyhedron structure  110  and four photo diodes  122 . Each of the polyhedron structure  110  overlaps with four photo diodes  122  as described in  FIG.  1   . The second pixel array  100 B includes one polyhedron structure  110 I and eight photo diodes  122  arranged as a 4x2 array. The polyhedron structure  110 I has a rectangular top facet  114 I and a rectangular bottom facet  112 I. The polyhedron structure  110  and the polyhedron structure  110 I are both Hexahedron, but a volume of the polyhedron structure  110 I is greater than a volume of the polyhedron structure  110 . In other words, a volume of the polyhedron structure  110  of the first pixel array  100 A is different from a volume of the polyhedron structure  110 I of the second pixel array  100 B. An area of the bottom facet  112  (see  FIG.  2   ) of the polyhedron structure  110  of the first pixel array  100 A is different from an area of the bottom facet  112 I of the polyhedron structure  110 I of the second pixel array  100 B. An area of the top facet  114  (see  FIG.  1   ) of the polyhedron structure  110  of the first pixel array  100 A is different from an area of the top facet  114 I of the polyhedron structure  110 I of the second pixel array  100 B. 
     As shown in  FIG.  12 B , the image sensor  10   j  is similar to the image sensor  10   i  shown in  FIG.  12 A , and the difference is that the top facet  114   m  of the polyhedron structure  110   m  has an elliptical shape. In other words, the polyhedron structure  110  of the first pixel array  100 A and the polyhedron structure  110   m  of the second pixel array  100 B have different shapes. 
     As shown in  FIG.  12 C , the image sensor  10   k  includes twelve first pixel array  100 A and one second pixel array  100 B. The second pixel array  100 B has one polyhedron structure  110   n  and sixteen photo diodes  122  arranged as a 4x4 array. The polyhedron structure  110   n  has a circular top facet  114   n  and a rectangular bottom facet  112   n . The polyhedron structure  110   n  has an octagonal column shape. In other words, a number of the side facets  116  of the polyhedron structure  110  of the first pixel array  100 A is different from a number of the side facets  116   n  of the polyhedron structure  110   n  of the second pixel array  100 B. 
       FIGS.  13 A to  13 C  are top view of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  13 A , the image sensor  10 I includes four first pixel arrays  100 . Each of the first pixel arrays  100  has a polyhedron structure  110   o  and four pixels  12 . The image sensor  10 I has a RGGB mosaic pattern. The upper-right first pixel array  100  has a blue color filter  130 B, and the lower-left first pixel array  100  has a red color filter  130 R. The other first pixel arrays  100  each has a green color filter  130 G. In the present embodiment, the size of each of the polyhedron structure  110   o  is smaller than the size of the underlying layers. For example, as shown in the upper-right first pixel array  100 , an area of an orthogonal projection of the polyhedron structure  110   o  is smaller than an area of the blue color filter  130 B. 
     As shown in  FIG.  13 B , the image sensor  10   m  is similar to the image sensor  10 I shown in  FIG.  13 A , and the difference is that the image sensor  10   m  has three polyhedron structures  110   o  and one polyhedron structure  110 . The polyhedron structure  110  is located above the blue color filter  130 B. The size of the polyhedron structure  110  is greater than the sizes of the polyhedron structures  110   o . In the present embodiment, an area of an orthogonal projection of the polyhedron structure  110  on the blue color filter  130 B is substantially the same as the area of blue the color filter  130 B. With such design, energy efficiency of each of the pixel arrays  100  can be adjusted based on the color filter arrangement so as to improve performance of the image sensor  10   m . 
     As shown in  FIG.  13 C , the image sensor  10   n  is similar to the image sensor  10   m  shown in  FIG.  13 B , and the difference is that the image sensor  10   n  has two polyhedron structures  110   o , one polyhedron structure  110 , and one polyhedron structure  110   p  above the red color filter  130 R. The size of the polyhedron structure  110   p  is smaller than the sizes of the polyhedron structures  110   o  and the size of the polyhedron structures  110 . With such design, energy efficiency of each of the pixel arrays  100  can be adjusted based on the color filter arrangement so as to improve performance of the image sensor  10   m . 
       FIG.  14 A  is a side view of an image sensor  10   o  according to one embodiment of the present disclosure.  FIG.  14 B  is a top view of the image sensor  10   o  in  FIG.  14 A . Reference is made to  FIG.  14 A  and  FIG.  14 B , the image sensor  10   o  includes a first pixel array  100 A and a second pixel array  100 B. Each of the first pixel array  100 A and the second pixel array  100 B includes four photo diodes  122 , a polyhedron structure  110 , and a color filter  130  located between the photo diodes  122  and the polyhedron structure  110 . The image sensor  10   o  further includes a grid  160  located between the color filters  130  of the first pixel array  100 A and the second pixel array  100 B. The polyhedron structure  110  has a translational shift relative to the color filter  130  and the photo diodes  122 . 
     As shown in  FIG.  14 B , an orthogonal projection of the polyhedron structure  110  of the first pixel array  100 A overlaps with the color filter  130  of the second pixel arrays  100 B and the gird  160 . As shown in  FIG.  14 A , the incident L 1  can be divided into two light beams L 2 , L 3  by the polyhedron structure  110  of the first pixel array  100 A. The light beam L 3  travels toward the photo diodes  122  of the second pixel array  100 B, and the light beam L 2  travels toward the photo diodes  122  of the first pixel array  100 A. Accordingly, the image sensor  10   o  and the image sensor  10  have the same advantages. 
     As shown in  FIG.  14 B , a displacement  d   1  between a center C 1  of the polyhedron structure  110  of the first pixel array  100 A and a center C 3  of the first pixel array  100 A in the plan view is the same as a displacement  d   2  between a center C 2  of the polyhedron structure  110  of the second pixel array  100 B and a center C 4  of the second pixel array  100 B in the plan view. In some other embodiments, the displacement  d   1  and the displacement  d   2  can be different. 
       FIG.  14 C  and  FIG.  14 D  are top views of the image sensors according to some embodiments of the present disclosure. As shown in  FIG.  14 C , the image sensor  10   p  includes a blue color filter  130 B, a red color filter  130 R, and two green color filters  130 G. In the present embodiment, a displacement  d   3  between the center of the polyhedron structures  110  and the center of the first pixel array  100 A is different from a displacement  d   4  between a center of the polyhedron structure  110  of the second pixel array  100 B and a center of the second pixel array  100 B. In other words, the displacement  d   3  between the polyhedron structure  110   q  and the first pixel array  100 A having a blue color is different from the displacement  d   4  between the polyhedron structure  110   r  and the second pixel array  100 B having a red color. As shown in  FIG.  14 D , the image sensor  10   q  is similar to the image sensor  10   q . The displacement  d   5  and the displacement  d   6  are different from the displacement  d   3  and the displacement  d   4  based on the ray direction R of the incident light. In other words, the polyhedron structures  110  can have independent displacements relative to the centers of the pixel arrays. Accordingly, the displacements can be adjusted based on a ray direction R of the incident light and a color filter arrangement. With such configuration, the performance of the image sensor  10   p  and the image sensor  10   q  can be improved. 
       FIGS.  15 A to  15 E  are cross-sectional views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  15 A , the image sensor  10   r  includes two first pixel arrays  100 . Each of the first pixel arrays  100  includes four photo diodes  122 , a color filter  130 , and a polyhedron structure  110 . The image sensor  10   r  further includes a grid  160  surrounding the color filters  130 . The grid  160  includes a body portion  162  and a metal layer portion  164 . The metal layer portion  164  is located between the body portion  162  and the photo diodes  122 . In some embodiments, a refractive index of the body portion  162  is greater than 1.5. In some other embodiments, a refractive index of the body portion  162  is greater than or equal to 1.0 and is smaller than 1.5. 
     As shown in  FIG.  15 B , the image sensor  10   s  is similar to the image sensor  10   r , and the difference is that the grid  160   a  of the image sensor  10   s  has no metal layer portion  164 . The refractive index of the grid  160   a  is greater than or equal to 1.0 and is smaller than 1.5. Since the grid  160   a  has no metal layer and the refractive index is lower, the efficiency of the image sensor  10   s  can be improved. 
     As shown in  FIG.  15 C , the image sensor  10   t  is similar to the image sensor  10   s  as shown in  FIG.  15 B , and the difference is that the grid  160   b  of the image sensor  10   t  includes a first layer  166  and a second layer  168 , and the refractive indexes materials of the first layer  166  and the second layer  168  are different. For example, the refractive index of second layer  168  is greater than 1.5, and the refractive index of the first layer  166  is greater than or equal to 1.0 and is smaller than 1.5. In the present embodiment, the second layer  168  covers and surrounds the first layer  166 . In other words, the first layer  166  is embedded in the second layer  168 . Since the effective refractive index of the grid  160   b  is lower, the efficiency of the image sensor  10   t  can be improved. 
     As shown in  FIG.  15 D , the image sensor  10   u  is similar to the image sensor  10   t  as shown in  FIG.  15 C , and the difference is the configuration of the grid  160   c . In the present embodiment, the first layer  166  of the grid  160   c  is located above the second layer  168  of the grid  160   c  of the image sensor  10   u . Since the refractive index of the grid  16   c  is lower, the efficiency of the image sensor  10   u  can be improved. 
     As shown in  FIG.  15 E , the image sensor  10   v  is similar to the image sensor  10   u  as shown in  FIG.  15 D , and the difference is the configuration of the grid  160   d . In the present embodiment, the second layer  168  of the grid  160   d  has a greater diameter than a diameter of the first layer  166  of the grid  160   d . Since the refractive index of the grid  160   d  is lower, the efficiency of the image sensor  10   v  can be improved. 
       FIGS.  16 A to  16 E  are top views of color arrangement of the color filters of the image sensors according to some embodiments of the present disclosure. Each pixel arrays  100  shown in  FIGS.  16 A to  16 E  are substantially the same as the pixel array shown in  FIG.  1    and  FIG.  2   . For convenience, only colors of the color filters are demonstrated herein, and the polyhedron structures and the photo diodes are omitted in  FIGS.  16 A to  16 E . As shown in  FIG.  16 A , the image sensor  20  has a RGGB arrangement. That is, the image sensor  20  includes color filters corresponding to red, green, and blue. As shown in  FIG.  16 B , the image sensor  20   a  has a RGBW arrangement. That is, the image sensor  20   a  includes color filters corresponding to red, green, blue, and white. As shown in  FIG.  16 C , the image sensor  20   b  has a CYYM arrangement. That is, the image sensor  20   b  includes color filters corresponding to cyan, yellow, and magenta. As shown in  FIG.  16 D , the image sensor  20   c  has a RYYB arrangement. That is, the image sensor  20   c  includes color filters corresponding to red, yellow, and blue. As shown in  FIG.  16 E , the image sensor  20   d  has a RGBIR arrangement. That is, the image sensor  20   d  includes color filters corresponding to red, green, blue, and infrared. 
       FIGS.  17 A to  17 D  are top views of image sensors according to some embodiments of the present disclosure. For convenience, only colors of the color filters are demonstrated herein. As shown in  FIG.  17 A , the image sensor  20   e  includes four fifth pixel arrays  100   e . Each of the fifth pixel arrays  100   e  includes four pixels and has a RGGB arrangement. In other words, the polyhedron structure  110  of each of the fifth pixel array  100   e  overlaps with four photo diodes  122  and four color filters including different colors (red, green, and blue). That is, an orthogonal projection of each of the polyhedron structure  110  overlaps with the color filters having at least three colors. 
     As shown in  FIG.  17 B , the image sensor  20   f  includes four third pixel arrays  100   c . Each of the third pixel arrays  100   c  includes one polyhedron structure  110  and nine photo diodes  122  (i.e., nine pixels), and each of the third pixel arrays  100   c  has single color. In other words, the polyhedron structure  110  of each of the third pixel array  100   c  overlaps with nine photo diodes  122  and one color filter. The four third pixel arrays  100   c  of the image sensor  20   f  collectively form a RGGB arrangement as shown in  FIG.  16 A . In some other embodiments, the image sensor  20   f  can have other types of color arrangements such as those arrangements shown in  FIGS.  16 B to  16 E . 
     As shown in  FIG.  17 C , the image sensor  20   g  includes four fourth pixel arrays  100   d . Each of the fourth pixel arrays  100   d  includes sixteen photo diodes  122 , and each of the fourth pixel arrays  100   d  has single color. In other words, the polyhedron structure  110  of each of the fourth pixel array  100   d  overlaps with sixteen photo diodes  122  and color filter. The four fourth pixel arrays  100   d  of the image sensor  20   g  collectively form a RGGB arrangement as shown in  FIG.  16 A . In some other embodiments, the image sensor  20   g  can have other types of color arrangements such as those arrangements shown in  FIGS.  16 B to  16 E . 
     As shown in  FIG.  17 D , the image sensor  20   h  includes four sixth pixel arrays  100   f . Each of the sixth pixel arrays  100   f  is similar to the image sensor  20   e  shown in  FIG.  17 A , and the difference is that each of the sixth pixel arrays  100   f  has single color. In other words, four polyhedron structures  110  of each of the sixth pixel arrays  100   f  collectively overlap with one color filter. That is, an orthogonal projection of more than one polyhedron structure  110  overlaps with one color filter. The four sixth pixel arrays  100   f  of the image sensor  20   h  collectively form a RGGB arrangement as shown in  FIG.  16 A . In some other embodiments, the image sensor  20   h  can have other types of color arrangements such as those shown in  FIGS.  16 B to  16 E . 
     Alternatively, the sixth pixel arrays  100   f  in  FIG.  17 D  can be considered as a combination of a single color filter and four pixel arrays, and each of the pixel arrays includes one polyhedron structure  110  and four photo diodes  122 . Therefore, at least one of the polyhedron structures of these four pixel arrays overlaps with the same color filter. 
       FIG.  18    is an electromagnetic field simulation result.  FIG.  18    represents the electric field distributions on the photo diodes of an image sensor  10  as shown in  FIG.  1    and  FIG.  2    when the wavelength of an incident light is 450 nm (blue), 550 nm (green), and 650 nm (red), respectively. The image sensor  10  only has a polyhedron structure  110  and has no micro lens. The electric field distribution of the image sensor  10  shows multiple peaks, and positions of those peaks are correlated with the pixel arrangements. That is, energy of the incident light can be divided by the polyhedron structures of the image sensor  10  based on the pixel arrangement. As such, the energy received by each photo diodes  122  is even. Therefore, the configuration of the image sensor of the present disclosure can improve the performance of the photo diodes. 
       FIG.  19    is a schematic of a pixel array  300  according to one embodiment of the present disclosure. The pixel array  300  includes a polyhedron structure  310 , an under layer  340 , a photo photoelectric conversion layer  320  having four photo diodes  322 , and a color filter  330  located between the polyhedron structure  310  and the photo diodes  322 . The polyhedron structure  310  is a tetrahedron. An incident light travels along a ray direction R. A centroid  315   a  of the polyhedron structure  310   a , a center  335  of the color filter  330 , and a center  325  of the photo diodes  322  are arranged along the ray direction R of the incident light. In other words, all layers of the pixel array  300  are shifted based on a Chief Ray Angle (CRA). As such, the efficiency of the pixel array  300  can be improved. 
       FIG.  20 A  is a schematic of a light distribution on the polyhedron structure  310  according to one embodiment of the present disclosure. As shown in  FIG.  20 A , a normal N 1  of the vertex  313  of the polyhedron structure  310  points toward a second direction (vertical direction) Y. The incident light L 1  has a Chief Ray Angle of 30 degrees relative to the vertical direction Y (i.e., a direction of an optical axis). As shown by the range R 1  and the range R 2 , the side facet  316 A (shady side) is less exposed by the incident light, and the side facet  316 B (bright side) is more exposed by the incident light. As a result, the amount of the light that can be refracted by the side facet  316 A and the side facet  316 B is uneven. In other words, energy distribution of the incident light L 1  after passing through the polyhedron structure  310  is uneven. 
       FIG.  20 B  is a schematic of a light distribution on the polyhedron structure  310  according to one embodiment of the present disclosure. As shown in  FIG.  20 B , a normal N 2  of the vertex  313   a  of the polyhedron structure  310   a  points toward a direction parallel with the ray direction R of the incident light L 1 . As a result, the range R 3  and the range R 4  are equal. Therefore, the side facet  316 A and the side facet  316 B of the polyhedron structure  310   a  are equally exposed by the incident light L 1 , and energy distribution of the incident L 1  after passing through the polyhedron structure  310   a  is even. In some other embodiments, a normal of the top facet of the polyhedron structure is parallel with the ray direction R. Accordingly, the shift of the normal of the vertex or the top facet of the polyhedron structure based on the ray direction (i.e., CRA) can improve performance of the image sensor. 
       FIG.  21 A  and  FIG.  21 B  are top views of an image sensor  30  according to one embodiment of the present disclosure. The image sensor  30  includes twenty-five photo diodes  322  arranged as a 5x5 array. Each photo diodes  322  overlaps with one polyhedron structure  310 ,  310   a ,  310   b . The polyhedron structures are omitted in  FIG.  21 A . When an incident light travel towards the center C 5  of the image sensor  30 . Ray directions R relative to each photo diodes  322  are represented by arrows. Specifically, the CRA for each photo diodes  322  is greater when the distance between the center C 5  and the photo diodes  322 . 
     As shown in  FIG.  21 B , all the polyhedron structure  310   a  follow the rules demonstrated in  FIG.  20 B . For example, four polyhedron structures  310   a  located at the corners of the image sensor  30  have a CRA of 30 degrees as described in  FIG.  30 B . The vertexes  313   a  of the polyhedron structures  310   a  shift towards the center C 5  of the image sensor  30 . The nine polyhedron structures  310   b  located at the outer part of the image sensor and located between the polyhedron structure  310   a  have a CRA smaller than 30 degrees. The vertexes  313   b  of the polyhedron structures  310   b  shift towards the center C 5 . Similarly, the polyhedron structures  310   c  located at the corners of an inner part of the image sensor  30  have a smaller CRA, and therefore the shifts of the vertexes  313   c  are smaller. The polyhedron structures  310   d  located between the polyhedron structures  310   c , and the shifts of the vertexes  313   d  are smaller than the shifts of the vertexes  313   c . The polyhedron structure  310  located at the center C 5  of the image sensor is substantially the same as the polyhedron structure  310  as shown in  FIG.  20 A . Accordingly, the further the polyhedron structures away from the center C 5 , the more the vertexes shift. As such, shifts of the vertexes form a concentric circle. With such design, the efficiency of the image sensor  30  can be improved. 
       FIG.  22    is a schematic of a first pixel array  400  according to one embodiment of the present embodiment. The first pixel array  400  includes a polyhedron structure  410 , a photo photoelectric conversion layer  420  having four photo diodes  422 , a color filter  430  located between the polyhedron structure  410  and the photo diodes  422 , and a micro lens  460  located between the polyhedron structure  410  and the color filter  430 . The polyhedron structure  310  is a tetrahedron. The light beams divided by the polyhedron structure  410  can be focused on the photo diodes  422  through the micro lens  460 . 
       FIG.  23    is a plot of relation between focusing separation distance and a height H2 of polyhedron structure. As shown in  FIG.  22   , the height H2 is the distance between the bottom facet  412  and the vertex  413 . The curves S 1 ~S 3  respectively represents the focusing separation distance when the refractive indexes of the polyhedron structure  410  are 1.25, 1.35, and 1.45, respectively. The refractive index of the micro lens  460  is 1.68. Accordingly, when the height H2 is fixed, suitable focusing separation distances can be determined by controlling the refractive index of the polyhedron structure  410 . 
       FIGS.  24 A to  24 D  are illuminance diagrams of the photo diodes  422  with various height H of the polyhedron structure  410 . The illuminance diagrams in  FIGS.  24 A to  24 D  are derived when the height H2 (see  FIG.  22   ) of the polyhedron structure  410  are 0.18 um, 0.28 um, 0.38 um, and 0.48 um, respectively. -Based on those results shown in  FIG.  23    and  FIGS.  24 A to  24 D , suitable focusing separation distances can be determined by controlling the height H2 and the refractive index of the polyhedron structure  410 . 
       FIG.  25 A  and  FIG.  25 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  25 A , the image sensor  40   a  includes sixteen first pixel array  400  as shown in  FIG.  22    arranged as a 4x4 array. The micro lenses  460  respectively overlap with the polyhedron structures  410 . As shown in  FIG.  25 B , the image sensor  40   b  is similar to the image sensor  40   a , and the difference is that each of the micro lenses  460  overlap with twenty-five photo diodes  422  which are arranged as a 5x5 array. In some other embodiments, the configuration of the photo diodes  422  under each of the micro lenses  460  can be different, such as a 3x3 array or a 4x4 array. 
       FIG.  26 A  and  FIG.  26 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  26 A , the image sensor  40   c  has nine micro lenses  460 , nine polyhedron structures  410   a , and eighty-one photo diodes  422  (i.e., eighty-one pixels). The micro lenses  460  respectively overlap with the polyhedron structures  410   a . Each of the polyhedron structures  410   a  has eight side facets  416 , a square bottom facet  412  and a circular top facet  414  that are similar to the polyhedron structure  110   j  shown in  FIG.  10 A . Each of the polyhedron structures  410   a  overlaps with nine photo diodes  422  arranged as a 3x3 array. Therefore, a sum of a number of the side facets  416  and a number of the top facet  414  of the polyhedron structure  410   a  equals to the number of the photo diodes  422 . 
     As shown in  FIG.  26 B , the image sensor  40   d  has four micro lenses  460 , four polyhedron structures  410   b , and sixty-four photo diodes  422 . The polyhedron structures  410   b  are similar to the polyhedron structures  110   k  shown in  FIG.  10 C . The micro lenses  460  respectively overlap with the polyhedron structures  410   b . Each of the polyhedron structures  410   b  overlaps with sixteen photo diodes  422  arranged as a 4x4 array. Therefore, a number of the side facets  416  of the polyhedron structure  410   b  equals to the number of the photo diodes  422 . 
     In the embodiments shown in  FIG.  26 A  and  FIG.  26 B , the polyhedron structure  410   a  and the polyhedron structure  410   b  are prisms. The energy of an incident light can be distributed more uniformly to the one or more pixels underlying the top fact  414  and the pixels underlying the side facets  416 . 
       FIG.  27 A  and  FIG.  27 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  27 A , the image sensor  40   e  includes fourteen first pixel arrays  400 A and one second pixel array  400 B. The first pixel array  400 A is similar to the pixel array  400  shown in  FIG.  22   . The second pixel array  400 B includes one micro lens  460   a  overlaps with eight photo diodes  422  arranged as a 4x2 array, and the second pixel array  400 B has no polyhedron structure. As shown in  FIG.  27 B , the image sensor  40   f  includes twelve first pixel array  400 A and one second pixel arrays  400 B. The second pixel array  400 B includes one micro lens  460   a  overlaps with sixteen photo diodes  422  arranged as a 4x4 array, and the second pixel array  400 B has no polyhedron structure. The configuration of the image sensor  40   e ,  40   f  can be utilized for specific functions such as auto focus function. 
       FIGS.  28 A to  28 C  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  28 A , the image sensor  40   g  includes fourteen first pixel array  400 A and one second pixel array  400 B. The first pixel array  400 A is similar to the pixel array  400  shown in  FIG.  22   . The second pixel array  400 B includes one polyhedron structure  410   c , one micro lens  460   c , and eight photo diodes  422  arranged as a 4x2 array. The micro lens  460   c  and the micro lens  410  have different shapes. A volume of the micro lens  460   c  is greater than a volume of the micro lens  460 . The polyhedron structure  410   c  and the polyhedron structure  410  are both tetrahedron, and a volume of the polyhedron structure  410   c  is greater than a volume of the polyhedron structure  410 . In other words, a volume of the polyhedron structure  410  of the first pixel array  400 A is different from a volume of the polyhedron structure  410   c  of the second pixel array  400 B. 
     As shown in  FIG.  28 B , the image sensor  40   h  includes twelve first pixel array  400 A and one second pixel array  400 B. The second pixel array  400 B includes one polyhedron structure  410   d , one micro lens  460   d , and sixteen photo diodes  422  arranged as a 4x4 array. A volume of the micro lens  460   d  is greater than a volume of the micro lens  460 . The top facet  414   d  of the polyhedron structure  410   d  has a circular shape. In other words, the polyhedron structure  410   d  and the polyhedron structure  410  have different shapes. 
     As shown in  FIG.  28 C , the image sensor  40   i  includes fourteen first pixel array  400 A and one second pixel array  400 B. The second pixel array  400 B has one polyhedron structure  410   e , one micro lens  460   e , and eight photo diodes  422  arranged as a 4x2 array. The polyhedron structure  410   e  has an elliptical top facet  414   e  and eight side facet  416   e . The polyhedron structure  110   n  has an octagonal column shape. In other words, a number of the side facets  416  (see  FIG.  22   ) of the polyhedron structure  410  of the first pixel array  100 A is different from a number of the side facets  416   e  of the polyhedron structure  410   e  of the second pixel array  100 B. 
       FIG.  29 A  and  FIG.  29 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  29 A , the image sensor  40   i  includes twelve first pixel array  400 A and on second pixel array  400 B. The first pixel array  400 A is similar to the pixel array  400  shown in  FIG.  22   . The second pixel array  400 B includes four polyhedron structures  410 , one micro lens  460   f , and sixteen photo diodes  422  arranged as a 4x4 array. In other words, a total number of the micro lens  460  and the micro lens  460   f  is different from a number of the polyhedron structures  410 . 
     As shown in  FIG.  29 B , the image sensor  40   j  is similar to the image sensor  40   i , and the difference is that the second pixel array  400 B includes one polyhedron  410   f  and four micro lenses  460 . In other words, a number of the micro lenses  460  is different from a total number of the polyhedron structures  410   
       FIG.  30 A  and  FIG.  30 B  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  30 A , the image sensor  40   k  includes sixty-four polyhedron structures  410   g  and sixteen micro lenses  460 . Each of the polyhedron structures  410   g  overlaps with one photo diodes  422  (i.e., one pixel). One micro lens  460  overlaps with four polyhedron structures  410   g  and four photo diodes  422 . As shown in  FIG.  30 B , the image sensor  40 I is similar to the image sensor  40   k , and the difference is that each of the micro lens  460   h  overlaps with nine polyhedron structures and nine photo diodes  422 . 
       FIGS.  31 A to  31 E  are top views of color arrangement of the color filters of the image sensors according to some embodiments of the present disclosure. Reference is made to  FIG.  22   , and  FIGS.  31 A to  31 E . The image sensors shown in  FIGS.  31 A to  31 E  all include four polyhedron structures  410  and four micro lenses  460  as described in  FIG.  22   . Each of the micro lenses  460  or the polyhedron structures  410  overlaps with multiple photo diodes  422 , and a 2x2 array is demonstrated herein merely as an example. 
     As shown in  FIG.  31 A , the image sensor  50  has a RGGB arrangement. That is the image sensor  50  includes color filters corresponding to red, green, and blue. As shown in  FIG.  31 B , the image sensor  50   a  has a RGBW arrangement. That is, the image sensor  50   a  includes color filters corresponding to red, green, blue, and white. As shown in  FIG.  31 C , the image sensor  50   b  has a CYYM arrangement. That is, the image sensor  50   b  includes color filters corresponding to cyan, yellow, and magenta. As shown in  FIG.  31 D , the image sensor  50   c  has a RYYB arrangement. That is, the image sensor  50   c  includes color filters corresponding to red, yellow, and blue. As shown in  FIG.  31 E , the image sensor  50   d  has a RGBIR arrangement. That is, the image sensor  50   d  includes color filters corresponding to red, green, blue, and infrared. 
       FIGS.  32 A to  32 D  are top views of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  32 A , the image sensor  50   e  includes four fifth pixel arrays  400   e . Each of the fifth pixel arrays  400   e  includes four pixels and has a RGGB arrangement. In other words, the polyhedron structure  410  of each of the fifth pixel array  400   e  overlaps with four photo diodes  122  and four color filters including different colors (red, green, and blue). That is, an orthogonal projection of each of the polyhedron structure  410  overlaps with the color filters having at least three colors. 
     As shown in  FIG.  32 B , the image sensor  50   f  includes four third pixel arrays  400   c . Each of the third pixel arrays  400   c  includes nine pixels and has single color. In other words, the polyhedron structure  410  of each of the third pixel arrays  400   c  is overlapped with nine photo diodes  422  and one color filter. The four third pixels arrays  400   c  of the image sensor  50   f  collectively form a RGGB arrangement as shown in  FIG.  31 A . In some other embodiments, the image sensor  50   f  can have other types of color arrangements such as those shown in  FIGS.  31 B to  31 E . 
     As shown in  FIG.  32 C , the image sensor  50   g  includes four fourth pixel arrays  400   d . Each of the fourth pixel arrays  400   d  includes sixteen pixels and has single color. In other words, the polyhedron structure  410  of each of the fourth pixel arrays  400   d  overlaps with sixteen photo diodes  422  and one color filter. The four fourth pixels arrays  400   d  of the image sensor  50   g  collectively form a RGGB arrangement as shown in  FIG.  31 A . In some other embodiments, the image sensor  50   g  can have other types of color arrangements such as those shown in  FIGS.  31 B to  31 E . 
     As shown in  FIG.  32 D , the image sensor  50   h  includes four sixth pixel arrays  400   f . Each of the sixth pixel arrays  400   f  is similar to the image sensor  50   e  shown in  FIG.  32 A , and the difference is that each of the sixth pixel arrays  400   f  has single color. In other words, four polyhedron structures  410  of each of the sixth pixel arrays  100   f  overlap with one color filter. That is, an orthogonal projection of more than one polyhedron structure  410  overlaps with one color filter. The four sixth pixels arrays  400   f  of the image sensor  50   h  collectively form a RGGB arrangement as shown in  FIG.  31 A . In some other embodiments, the image sensor  50   h  can have other types of color arrangements such as those shown in  FIGS.  31 B to  31 E . 
       FIG.  33 A  is a partial top view of an image sensor according to one embodiment of the present disclosure.  FIG.  33 B  is a cross-sectional view taken along line  33 B- 33 B in  FIG.  33 A . As shown in  FIG.  34 A , a polyhedron structure  410   h  includes edges  417   h  formed between adjacent two of the side facets  416   h . The photo diodes  422  are arranged along a first direction X (horizontal) and a second direction Y (vertical) perpendicular to the first direction X. Therefore, orthogonal projections of the edges  417   h  extend along the first direction X or the second direction Y. 
     Reference is made to  FIG.  22    and  FIG.  25 A . Orthogonal projections of the edges  417  of the polyhedron structure  410  extend along the directions different from the first direction X or the second direction Y. In the embodiment in  FIG.  22   , the orthogonal projections of the edges  417  extend along diagonal directions. Therefore, comparing with the polyhedron structure  410  as shown in  FIG.  22   , the polyhedron structure  410   h  shown in  FIG.  33 A  are rotated 90 degrees with a rotation axis parallel with the third direction Z. With such configuration, the side facets  416  face the photo diodes  422  so as to improve the focusing ability. As shown in  FIG.  34 B , two polyhedron structure  410   h  are connected together, and there is a side wall  419   h  located between adjacent two polyhedron structures  410   h . 
       FIG.  33 C  and  FIG.  33 D  are top view of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  33 C , the image sensor  60  includes sixteen polyhedron structures  410   h  and sixteen micro lenses  460 . Each of the polyhedron structure  410  and the micro lens  460  overlaps with four photo diodes  422 . The edges  417  are extend along the first direction X and the second direction Y, and the vertexes  413  overlaps the centers of the micro lenses  460 . The side wall  419   h  overlaps with an interface between two micro lens  460 . As shown in  FIG.  33 D , the image sensor  60   a  is similar to the image sensor  60 , and the difference is that each of the micro lenses  460  overlaps with twenty-five photo diodes  422 . The image sensor  60   a  can has similar advantages as those of the image sensor  60 , and the description is not repeated hereinafter. 
       FIG.  34    is a schematic of optical path when an incident light traveling through the polyhedron structure  410   i . In the present embodiment, the vertex  413   i  of the polyhedron structure  410   i  is shifted. For example, an orthogonal projection of the vertex  413   i  is located between the first pixel array  400 A and the second pixel array  400 B. With such configuration, an incident light L 1  can be divided into light beams L 2 , L 3  focused in the photo diodes  422  to improve performance of the photo diodes  422 . Therefore, the first pixel array  400 A and the second pixel array  400 B of the present embodiment can have the similar advantages as those of the pixel array  400  shown in  FIG.  22   , and the description is not repeated hereinafter. 
       FIG.  35 A  is a partial top view of an image sensor according to one embodiment of the present disclosure.  FIG.  35 B  and  FIG.  35 C  are top view of image sensors according to some embodiments of the present disclosure. As shown in  FIG.  35 A , a polyhedron structure  410   i  includes edges  417   i  formed between adjacent two of the side facets  416   i . The polyhedron structure  410   i  partially overlaps with four micro lenses  460 . A vertex  413   i  of the polyhedron structure  410   i  is located at the position surrounded by these four adjacent micro lenses  460 . 
     As shown in  FIG.  35 B , the image sensor  60   b  includes sixteen polyhedron structures  410   i  and sixteen micro lenses  460 . Each of the polyhedron structure  410   i  and the micro lens  460  overlaps with four photo diodes  422 . The edges  417   i  are extend along the first direction X and the second direction Y, and the vertexes  413   i  are located at the position surrounded by four adjacent micro lenses  460 . As shown in  FIG.  35 C , the image sensor  60   c  is similar to the image sensor  60   b , and the difference is that each of the micro lenses  460   i  overlaps with nine photo diodes  422 . The image sensor  60   c  can has similar advantages as those of the image sensor  60   b , and the description is not repeated hereinafter. 
       FIGS.  36 A to  36 C  are cross-sectional view of pixel arrays according to some embodiments of the present disclosure. As shown in  FIG.  36 A , the pixel array  70  includes a color filter  430 , a micro lens  460 , and a polyhedron structure  410 . The polyhedron structure  410  is directly formed on the micro lens  460 , and there is no other layer formed on the polyhedron structure  410 . Under this condition, a refractive index of the micro lens  460  is greater than an refractive index of the polyhedron structure  410 , and the refractive index of the polyhedron structure  410  is greater than 1.1 (i.e., the refractive index of air). 
     As shown in  FIG.  36 B , the pixel array  70   a  is similar to the pixel array  70 , and the difference is that the pixel array  70   a  further includes an index matching layer  470  located between the micro lens  460  and the polyhedron structure  410 . Under this condition, the refractive index of the index matching layer is smaller than the refractive index of the micro lens  460  and is greater than the refractive index of the polyhedron structure  410 . As such, light transmission efficiency and performance of the photo diodes  422  can be improved. 
     As shown in  FIG.  36 C , the pixel array  70   b  is similar to the pixel array  70   a , and the difference is that the pixel array  70   b  further includes a first antireflection layer  480 , a second antireflection layer  482 , and an index changing layer  490 . The first antireflection layer  480  is coated on the polyhedron structure  410 . The second antireflection layer  482  is located between the polyhedron structure  410  and the index changing layer  490 . The index changing layer  490  is located between the second antireflection layer  482  and the micro lens  460 . Under this condition, the refractive index of the polyhedron structure  410  is greater than the refractive index of the index changing layer  490  and is smaller than or equal to the refractive index of the micro lens  460 . As such, light transmission efficiency and performance of the photo diodes  422  can be improved. 
       FIG.  37    is an electromagnetic field simulation result. Data in the first row represent the electric field distributions on the photo diodes of an image sensor having the pixel array  400  as shown in  FIG.  22    when the wavelength of an incident light is 450 nm (blue), 550 nm (green), and 650 nm (red), respectively. Data in the second row represent the electric field distributions on the photo diodes of an image sensor having the pixel array as shown in  FIG.  34   . As shown in  FIG.  37   , the electric field distribution of the image sensor show multiple peaks, and positions of those peaks are correlated with the pixel arrangements. That is, energy of the incident light can be divided by the polyhedron structure of the image sensor based on the pixel arrangement. As such, the energy received by each photo diodes  422  is even. In addition, even there is a shift between the polyhedron structure and the micro lens or the photo diodes, performance of the photo diodes can still be improved. 
     In summary, the polyhedron structure is configured to divide an incident light into multiple light beams towards the photo diodes. In addition, a number of the light beam can be determined by a number of the side facets of the polyhedron structure. A position of the focus of the light beam can be determined by the area of the top facet of the polyhedron structure, the height of the polyhedron, or the refractive index of the polyhedron structure. As such, focuses of the light beams are positioned more correlated with positions of photo diodes. Therefore, performance of the photo diodes can be improved. 
     Although the present invention has been described in considerable detail with reference to certain embodiments thereof, other embodiments are possible. Therefore, the spirit and scope of the appended claims should not be limited to the description of the embodiments contained herein. 
     It will be apparent to those skilled in the art that various modifications and variations can be made to the structure of the present invention without departing from the scope or spirit of the invention. In view of the foregoing, it is intended that the present invention cover modifications and variations of this invention provided they fall within the scope of the following claims.