Patent Publication Number: US-9837582-B1

Title: Display device

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims priority of China Patent Application No. 201610307720.1, filed on May 11, 2016, the entirety of which is incorporated by reference herein. 
     BACKGROUND 
     Field of the Invention 
     The disclosure relates to a display device, and in one embodiment to a display device having a light-emitting diode chip. 
     Description of the Related Art 
     As digital technology develops, display devices are becoming more widely used in our society. For example, display devices have been applied in modern information and communication devices such as televisions, notebooks, computers, mobile phones, and smartphones. In addition, each generation of display devices has been developed to be thinner, lighter, smaller, and more fashionable than the last. These display devices include light-emitting diode display devices. 
     The recombination radiation of electron and hole in the light-emitting diode may produce electromagnetic radiation (such as light) through the current at the p-n junction. For example, in a forward bias p-n junction formed by direct band gap materials such as GaAs or GaN, the recombination of electron and hole injected into the depletion region results in electromagnetic radiation such as light. The aforementioned electromagnetic radiation may lie in the visible region or the non-visible region. Materials with different band gaps may be used to form light-emitting diodes of different colors. 
     Since mass production has recently become the tendency in the light-emitting diode industry, any increase in the yield of manufacturing light-emitting diodes will reduce costs and result in huge economic benefits. However, existing display devices have not been satisfactory in every respect. For example, when the light-emitting view angle and the light-emitting shape of the light-emitting diode display device have to be altered, an additional second lens layer needs to be disposed over the light-emitting surface. However, this greatly increases the cost. 
     Therefore, a display device which may alter the light-emitting view angle and the light-emitting shape freely or may improve the light-emitting effectiveness is needed. 
     BRIEF SUMMARY 
     The present disclosure provides a display device, including: a substrate; a light-emitting diode disposed over the substrate, wherein the light-emitting diode includes: a first conductive-type semiconductor layer, a light-emitting layer and a second conductive-type semiconductor layer, wherein the light-emitting layer is disposed between the first conductive-type semiconductor layer and the second conductive-type semiconductor layer, wherein the second conductive-type semiconductor layer is adjacent to the substrate, wherein the first conductive-type semiconductor layer includes a bulk portion and a reflection layer disposed over a side of the bulk portion, wherein the bulk portion has a first surface away from the light-emitting layer and a second surface adjacent to the light-emitting layer, and the second conductive-type semiconductor layer has a third surface adjacent to the light-emitting layer and a fourth surface away from the light-emitting layer. When viewed from a cross-sectional view, there is a specific relationship between the width of the first surface, the width of the light-emitting layer, the distance from the first surface to the fourth surface, and the distance from the first surface to the light-emitting layer. 
     A detailed description is given in the following embodiments with reference to the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The disclosure may be more fully understood by reading the subsequent detailed description and examples with references made to the accompanying drawings, wherein: 
         FIG. 1A  is a cross-sectional view of a display device in accordance with some embodiments of the present disclosure; 
         FIG. 1B  is a cross-sectional view of a display device in accordance with some embodiments of the present disclosure; 
         FIG. 2A  is a cross-sectional view of the reflection layer in accordance with some embodiments of the present disclosure; 
         FIG. 2B  is a cross-sectional view of the reflection layer in accordance with some embodiments of the present disclosure; 
         FIG. 3  is an analytical figure of the ratio of specific width and distance in the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 4A  is a schematic view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 4B  is an analytical figure of the width of the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 4C  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 4D  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 4E  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 4F  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 4G  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 5A  is a schematic view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 5B  is an analytical figure of the width of the major axis at the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 5C  is an analytical figure of the width of the minor axis at the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 5D  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 5E  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 5F  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 5G  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 5H  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 6A  is a schematic view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 6B  is an analytical figure of the width of the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 6C  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 6D  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 6E  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 6F  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 6G  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 7A  is a schematic view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 7B  is an analytical figure of the width of the major axis at the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 7C  is an analytical figure of the width of the minor axis at the bottom surface of the stack structure versus the half width at half maximum in accordance with some embodiments of the present disclosure; 
         FIG. 7D  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 7E  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 7F  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 7G  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 7H  is a distribution figure of the emitted light at various view angles in accordance with some embodiments of the present disclosure; 
         FIG. 8A  is a cross-sectional view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 8B  is a cross-sectional view of the stack structure in accordance with some embodiments of the present disclosure; 
         FIG. 9A  is a cross-sectional view of a display device in accordance with some other embodiments of the present disclosure; 
         FIG. 9B  is a cross-sectional view of a display device in accordance with some other embodiments of the present disclosure; and 
         FIG. 9C  is a cross-sectional view of a display device in accordance with some other embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The display device of the present disclosure is described in detail in the following description. In the following detailed description, for purposes of explanation, numerous specific details and embodiments are set forth in order to provide a thorough understanding of the present disclosure. The specific elements and configurations described in the following detailed description are set forth in order to clearly describe the present disclosure. It will be apparent, however, that the exemplary embodiments set forth herein are used merely for the purpose of illustration, and the inventive concept may be embodied in various forms without being limited to those exemplary embodiments. In addition, the drawings of different embodiments may use like and/or corresponding numerals to denote like and/or corresponding elements in order to clearly describe the present disclosure. However, the use of like and/or corresponding numerals in the drawings of different embodiments does not suggest any correlation between different embodiments. In addition, in this specification, expressions such as “first material layer disposed on/over a second material layer”, may indicate the direct contact of the first material layer and the second material layer, or it may indicate a non-contact state with one or more intermediate layers between the first material layer and the second material layer. In the above situation, the first material layer may not be in direct contact with the second material layer. 
     In addition, in this specification, relative expressions are used. For example, “lower”, “bottom”, “higher” or “top” are used to describe the position of one element relative to another. It should be appreciated that if a device is flipped upside down, an element that is “lower” will become an element that is “higher”. 
     The terms “about” and “substantially” typically mean +/−20% of the stated value, more typically +/−10% of the stated value, more typically +/−5% of the stated value, more typically +/−3% of the stated value, more typically +/−2% of the stated value, more typically +/−1% of the stated value and even more typically +/−0.5% of the stated value. The stated value of the present disclosure is an approximate value. When there is no specific description, the stated value includes the meaning of “about” or “substantially”. 
     It should be understood that, although the terms first, second, third etc. may be used herein to describe various elements, components, regions, layers, portions and/or sections, these elements, components, regions, layers, portions and/or sections should not be limited by these terms. These terms are only used to distinguish one element, component, region, layer, portion or section from another region, layer or section. Thus, a first element, component, region, layer, portion or section discussed below could be termed a second element, component, region, layer, portion or section without departing from the teachings of the present disclosure. 
     Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. It should be appreciated that, in each case, the term, which is defined in a commonly used dictionary, should be interpreted as having a meaning that conforms to the relative skills of the present disclosure and the background or the context of the present disclosure, and should not be interpreted in an idealized or overly formal manner unless so defined. 
     This description of the exemplary embodiments is intended to be read in connection with the accompanying drawings, which are to be considered part of the entire written description. The drawings are not drawn to scale. In addition, structures and devices are shown schematically in order to simplify the drawing. 
     In the description, relative terms such as “lower,” “upper,” “horizontal,” “vertical,”, “above,” “below,” “up,” “down,” “top” and “bottom” as well as derivative thereof (e.g., “horizontally,” “downwardly,” “upwardly,” etc.) should be construed to refer to the orientation as then described or as shown in the drawing under discussion. These relative terms are for convenience of description and do not require that the apparatus be constructed or operated in a particular orientation. Terms concerning attachments, coupling and the like, such as “connected” and “interconnected,” refer to a relationship wherein structures are secured or attached to one another either directly or indirectly through intervening structures, as well as both movable or rigid attachments or relationships, unless expressly described otherwise. 
     The term “substrate” is meant to include devices formed within a transparent substrate and the layers overlying the transparent substrate. All needed transistor elements may already be formed over the substrate. However, the substrate is represented with a flat surface in order to simplify the drawing. The term “substrate surface” is meant to include the uppermost exposed layers on a transparent substrate, such as an insulating layer and/or metallurgy lines. The material of the substrate may include glass, plastic or any other materials or layers which the wires or transistor elements may be formed on, such as polyimide (PI). The substrate may also be a flexible substrate. 
     In some embodiments of the present disclosure, since the specific width and distance in the stack structure of the light-emitting diode have a specific relationship, the light-emitting diode display device in some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely and/or may improve the light-emitting effectiveness. 
       FIG. 1A  is a cross-sectional view of a display device  100  in accordance with some embodiments of the present disclosure. As shown in  FIG. 1A , the display device  100  includes a substrate  102  and a light-emitting diode  104  disposed over the substrate  102 . In some embodiments of the present disclosure, the substrate  102  may include a thin film transistor substrate. 
     The light-emitting diode  104  may include the first conductive-type semiconductor layer  106 . The first conductive-type semiconductor layer  106  has a substrate portion  106 A and a bulk portion  106 B disposed over the substrate portion  106 A. The bulk portion  106 B has a first surface S 1  adjacent to the substrate portion  106 A and a second surface S 2  away from the substrate portion  106 A. In other embodiments of the present disclosure, the first conductive-type semiconductor layer  106  may only have a bulk portion  106 B and may not have a substrate portion  106 A. The bulk portion  106 B may be in direct contact with the conductive electrode. In this embodiment, the first surface S 1  is the bottom surface of the bulk portion  106 B. In this embodiment, the interface separating the bulk portion  106 B and the substrate portion  106 A serves as the datum surface of the bottom surface of the bulk portion  106 B. The datum surface is substantially parallel to the surface of the substrate portion  106 A. In this embodiment, the datum surface is a portion of the surface of substrate portion  106 A. 
     The light-emitting diode  104  may further include a light-emitting layer  108  disposed over the second surface S 2  of the bulk portion  106 B of the first conductive-type semiconductor layer  106 , and a second conductive-type semiconductor layer  110  disposed over the light-emitting layer  108 . In other words, the light-emitting layer  108  is disposed between the first conductive-type semiconductor layer  106  and the second conductive-type semiconductor layer  110 . The second conductive-type semiconductor layer  110  is adjacent to the substrate  102 . In addition, as shown in  FIG. 1A , the first surface S 1  of the bulk portion  106 B of the first conductive-type semiconductor layer  106  is away from the light-emitting layer  108 , and the second surface S 2  of the bulk portion  106 B of the first conductive-type semiconductor layer  106  is adjacent to the light-emitting layer  108 . In addition, the second conductive-type semiconductor layer  110  has a third surface S 3  adjacent to the light-emitting layer  108  and a fourth surface S 4  away from the light-emitting layer  108 . In some embodiments of the present disclosure, the area of the first surface S 1  is greater than the area of the fourth surface S 4 . In addition, the bulk portion  106 B, the light-emitting layer  108  and the second conductive-type semiconductor layer  110  together serve as a stack structure  112 . 
     The first conductive-type semiconductor layer  106  has the first conductive type. The first conductive-type semiconductor layer  106  may include, but is not limited to, doped In x Al y Ga (1−x−y )N, wherein 0≦x≦1, 0≦y≦1 and 0≦(x+y)≦1. For example, in some embodiments of the present disclosure, the first conductive-type semiconductor layer  106  may include, but is not limited to, doped GaN, InN, AlN, In x Ga (1−x) N, Al x In (1−x) N, Al x In y Ga (1−x−y) N or any other suitable materials, wherein 0≦x≦1, 0≦y≦1 and 0≦(x+y)≦1. The first conductive-type semiconductor layer  106  may be a P-type semiconductor layer, and may be formed by molecular beam epitaxy (MBE), metalorganic chemical vapor deposition (MOCVD), hydride vapor phase epitaxy (HVPE), liquid phase epitaxy or any other suitable epitaxy process. 
     The light-emitting layer  108  may include, but is not limited to, homojunction, heterojunction, single-quantum well (SQW), multiple-quantum well (MQW) or any other suitable structures. In some embodiments of the present disclosure, the light-emitting layer  108  may include undoped N-type In x Ga (1−x) N. In some embodiments of the present disclosure, the light-emitting layer  108  may include other materials such as Al x In y Ga (1−x−y) N. Moreover, the light-emitting layer  108  may include a multiple-quantum well structure with multiple-quantum layers (such as InGaN) and barrier layers (such as GaN) arranged alternately. Moreover, the light-emitting layer  108  may be formed by metalorganic chemical vapor deposition (MOCVD), molecular beam epitaxy (MBE), hydride vapor phase epitaxy (HVPE), liquid phase epitaxy (LPE) or any other suitable chemical vapor deposition process. The total thickness of the light-emitting layer  108  may range from about 5 nm to 200 nm. 
     The second conductive-type semiconductor layer  110  has the second conductive type which is different from the first conductive type. The second conductive-type semiconductor layer  110  may include, but is not limited to, doped In x Al y Ga (1−x−y) N, wherein 0≦x≦1, 0≦y≦1 and 0≦(x+y)≦1. For example, in some embodiments of the present disclosure, the second conductive-type semiconductor layer  110  may include, but is not limited to, doped GaN, InN, AlN, In x Ga (1−x) N, Al x In y Ga (1−x−y) N or any other suitable materials, wherein 0≦x≦1, 0≦y≦1 and 0≦(x+y)≦1. The second conductive-type semiconductor layer  110  may be N-type semiconductor layer, and may be formed by molecular beam epitaxy (MBE), metalorganic chemical vapor deposition (MOCVD), hydride vapor phase epitaxy (HVPE), liquid phase epitaxy or any other suitable epitaxy process. 
     In some embodiments of the present disclosure, a light-emitting material layer and a second conductive-type semiconductor material may be deposited over a first conductive-type semiconductor substrate (not shown), then a etching process is performed to form the substrate portion  106 A and the stack structure  112  disposed over the substrate portion  106 A and having a trapezoidal cross-section, as shown in  FIG. 1A . Therefore, in some embodiments of the present disclosure, the substrate portion  106 A and the bulk portion  106 B are formed in one piece. However, in other embodiments of the present disclosure, the substrate portion  106 A and the bulk portion  106 B may not be formed in one piece. 
     In some embodiments of the present disclosure, as shown in  FIG. 1A , the direction perpendicular to the first surface S 1  of the bulk portion  106 B is the first direction A 1 . When viewed from a cross-sectional view, the acute angle between the sidewall  112 S of the stack structure  112  and the first direction A 1  is the angle θ, and the angle θranges from about 1 to 89 degrees, for example from about 10 to 85 degrees, or from about 20 to 80 degrees, or from about 30 to 75 degrees, or from about 40 to 70 degrees, or from about 50 to 60 degrees, or from about 5 to 50 degrees according to design requirements. 
     Still referring to  FIG. 1A , the light-emitting diode  104  may further include a first electrode  114 A which is electrically connected to the first conductive-type semiconductor layer  106 . The light-emitting diode  104  may further include a second electrode  114 B which is electrically connected to the second conductive-type semiconductor layer  110 . In some embodiments of the present disclosure, the first electrode  114 A is disposed over the surface of the substrate portion  106 A of the first conductive-type semiconductor layer  106 . The second electrode  114 B is disposed over the fourth surface S 4  of the second conductive-type semiconductor layer  110 . In addition, in some embodiments of the present disclosure, the second electrode  114 B completely covers the fourth surface S 4  of the second conductive-type semiconductor layer  110 . In addition, in some embodiments of the present disclosure, the light-emitting diode  104  is bonded to the substrate  102  with the second electrode  114 B facing toward the substrate  102 . In some embodiments of the present disclosure, the second electrode  114 B may partially cover the fourth surface S 4  of the second conductive-type semiconductor layer  110  according to design requirements as long as the desired reflection design is achieved. 
     The material of the first electrode  114 A and the second electrode  114 B may independently include, but is not limited to, a single layer or multiple layers of nickel, copper, gold, indium tin oxide, indium, tin, titanium, a combination thereof, or any other metal material with good conductivity. In some embodiments of the present disclosure, the first electrode  114 A and the second electrode  114 B may be formed by chemical vapor deposition (CVD), sputtering, resistive thermal evaporation, electron beam evaporation, or any other suitable method. The chemical vapor deposition may include, but is not limited to, low-pressure chemical vapor deposition (LPCVD), low-temperature chemical vapor deposition (LTCVD), rapid thermal chemical vapor deposition (RTCVD), plasma enhanced chemical vapor deposition (PECVD), atomic layer deposition (ALD), or any other suitable method. 
     Still referring to  FIG. 1A , the light-emitting diode  104  may further include a reflection layer  116  disposed over the sidewall  112 S of the stack structure  112 . In other words, the reflection layer  116  may be disposed over the sidewall of the first conductive-type semiconductor layer  106  and the sidewall of the second conductive-type semiconductor layer  110  respectively. In other embodiments of the present disclosure, the reflection layer  116  may only be disposed over the sidewall of the bulk portion  106 A of the first conductive-type semiconductor layer  106 . As long as the reflection layer is disposed over at least some regions of the light-emitting path, the light-emitting shape may be altered or the light-emitting effectiveness may be improved. The reflection layer  116  may be optionally disposed over the substrate portion  106 B of the first conductive-type semiconductor layer  106 . In some embodiments of the present disclosure, the material of the reflection layer  116  may include metal and may be the same as or similar to that of the first electrode  114 A and the second electrode  114 B. However, in other embodiments of the present disclosure, the reflection layer  116  may be a Bragg reflection layer, and the material of the reflection layer  116  may be non-metal material or insulating material. For example, in some embodiments of the present disclosure, the material of the reflection layer  116  may be the insulating layer with low index of refraction such as SiO 2  or the insulating layer with high index of refraction such as SiN. The index of refraction may be tuned by altering the manufacturing variables or the component ratio, and the material of the reflection layer  116  is not limited to the aforementioned materials. 
     For example, as shown in  FIG. 2A , the reflection layer  116  which serves as the Bragg reflection layer may include a plurality of sub-reflection layers (for example, the sub-reflection layers  116 C 1 ,  116 C 2  and  116 C 3 ). Each of the sub-reflection layers (for example, the sub-reflection layers  116 C 1 ,  116 C 2  and  116 C 3 ) may sequentially include the reflection layer  116 D 1  and the reflection layer  116 D 2  with different index of refraction. In some embodiments of the present disclosure, the thicknesses of the reflection layer  116 D 1  and the reflection layer  116 D 2  may be less than or equal to about 0.25 times the optical wavelength (about ¼ the optical wavelength). In addition, in other embodiments of the present disclosure, as shown in  FIG. 2B , the reflection layer  116  which serves as the Bragg reflection layer may include a plurality of sub-reflection layers (for example, the sub-reflection layers  116 C 1  and  116 C 2 ). Each of the sub-reflection layers (for example, the sub-reflection layers  116 C 1  and  116 C 2 ) may sequentially include the reflection layer  116 D 1 , the reflection layer  116 D 2  and the reflection layer  116 D 3  with different index of refraction. In some embodiments of the present disclosure, the thicknesses of the reflection layer  116 D 1 , the reflection layer  116 D 2  and the reflection layer  116 D 3  may be less than or equal to about 0.25 times the optical wavelength (about ¼ the optical wavelength). 
     Still referring to  FIG. 1A , in some embodiments of the present disclosure, the reflection layer  116  is conformally disposed over the sidewall  112 S of the stack structure  112 . In addition, in some embodiments of the present disclosure, the reflection layer  116  may be in direct contact with the stack structure  112 . However, in other embodiments of the present disclosure, the reflection layer  116  may not be in direct contact with the stack structure  112 . An insulating layer may be disposed between the reflection layer  116  and the stack structure  112 . The material of the insulating layer is not limited. 
     In addition, in some embodiments of the present disclosure, as shown in  FIG. 1A , the reflection layer  116  does not come into contact with the second electrode  114 B. In other words, in this embodiment, if the reflection layer  116  is a conductive material, the reflection layer  116  and the second electrode  114 B are electrically isolated from each other. However, in other embodiments of the present disclosure, the reflection layer  116  may be in direct contact with the second electrode  114 B. 
     In addition, in some embodiments of the present disclosure, as shown in  FIG. 1A , the reflection layer  116 A disposed over the sidewall of the bulk portion  106 B of the stack structure  112  is not electrically connected to the reflection layer  116 B disposed over the sidewall of the second conductive-type semiconductor layer  110 . In other words, in this embodiment, if the reflection layer  116  and the reflection layer  116 B are made of conductive material, the reflection layer  116 A and the reflection layer  116 B are electrically isolated from each other. 
     Still referring to  FIG. 1A , the width of the first surface S 1  of the bulk portion  106 B is width D 1 , the width of the light-emitting layer  108  is width D 2 , the width of the fourth surface S 4  of the second conductive-type semiconductor layer  110  is the width D 3 , and the distance from the first surface S 1  to the fourth surface S 4  is the distance H 1 , which is also the thickness of the stack structure  112 . The distance from the first surface S 1  to the light-emitting layer  108  is the distance H 2 , which is also the height of the light-emitting layer  108  calculated from the first surface S 1 . The specific ratio R which includes the width D 1 , the width D 2 , the distance H 1  and the distance H 2  fit the following equation 1: 
     
       
         
           
             
               
                 
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     Since some embodiments of the present disclosure let the width D 1  of the first surface S 1  of the stack structure  112  of the light-emitting diode  104 , the width D 2  of the light-emitting layer  108 , the distance H 1  from the first surface S 1  to the fourth surface S 4  (namely the thickness of the stack structure  112 ), the distance H 2  from the first surface S 1  to the light-emitting layer  108  (namely the height of the light-emitting layer  108  calculated from the first surface S 1 ) has a relationship expressed by equation 1, the light-emitting diode display device of some embodiments of the present disclosure may freely alter the light-emitting view angle and the light-emitting shape or may improve the light-emitting effectiveness. In this embodiment, the reflection layer  116  is substantially disposed over the entire sidewall of the stack structure. Since the opening  117  of the reflection layer  116  at the light-emitting direction is the first surface S 1 , the first surface S 1  substantially coincide with the bottom surface of the stack structure. In other embodiments of the present disclosure, the size of the opening at the light-emitting direction is the size of the bottom surface of the reflection layer, and the opening  117  at the light-emitting direction is referred to as the first surface S 1 , therefore, the first surface S 1  may not coincide with the bottom surface of the stack structure. In other words, referring to  FIG. 1B , when the reflection layer  116  does not completely cover the entire sidewall  112 S of the stack structure  112 , the first surface S 1  is defined by the datum surface formed by the opening  117  of the reflection layer  116  and may be substantially parallel to the surface of the substrate portion  106 A, but it&#39;s not limited thereto. In this embodiment, the first surface S 1  may not coincide with the bottom surface of the bulk portion  106 B. 
     In addition, since the additional second lens is not needed in the embodiments of the present disclosure to alter the light-emitting view angle and the light-emitting shape, the embodiments of the present disclosure may lower the cost of the light-emitting diode display device  100 . 
     In one embodiment,  FIG. 3  is an analytical figure of the aforementioned specific ratio R versus the half width at half maximum (HWHM) of the emitted light of the display device  100  in accordance with some embodiments of the present disclosure. The line with circle dots shows the relationship between the specific ratio R versus the half width at half maximum of the emitted light of the display device  100  when the first surface S 1  and the fourth surface S 4  have circular shapes in the top view. The line with square dots shows the relationship between the specific ratio R versus the half width at half maximum of the emitted light of the display device  100  when the first surface S 1  and the fourth surface S 4  have square shapes in the top view. In this embodiment, the specific ratio R may range from about 0.269 to 0.857 (0.269≦R≦0.857). 
     As shown in  FIG. 3 , when the ratio R is greater than or equal to 0.269 and is less than 0.3, the half width at half maximum is greater than or equal to +30° and is less than +45°. In this embodiment, the light shape is focus shape, and may be applied to the device which need a straight light such as an indicator light. 
     When the ratio R is greater than or equal to 0.3 and is less than 0.328, the half width at half maximum is greater than or equal to ±45. In this embodiment, the light shape is focus shape, and may be applied to a device which needs a straight light such as a headlight. 
     When the ratio R is greater than or equal to 0.328 and is less than 0.375, the half width at half maximum is greater than ±45° and is less than or equal to ±60°. In this embodiment, the light shape is fan-shape, and may be applied to the table lamp which need a uniform light. This embodiment may also solve the issue of non-uniformity of emitted light between two the light-emitting diodes. 
     When the ratio R is greater than or equal to 0.375 and is less than 0.49, the half width at half maximum is ±60°. In this embodiment, the light shape is between the fan-shape and Gaussian distribution, and may be applied to the table lamp which need a uniform light. This embodiment may also solve the issue of non-uniformity of emitted light between two the light-emitting diodes. 
     When the ratio R is greater than or equal to 0.49 and is less than 0.857, the half width at half maximum is ±50°. In this embodiment, the light shape is a Gaussian distribution, and may be applied to the package chip such as a surface-mount device light-emitting diode. For example, this embodiment may be applied to an edge lighting light source or a bottom-lighting light source. 
     In addition, the first surface S 1  of the bulk portion  106 B and the fourth surface S 4  of the second conductive-type semiconductor layer  110  may be any shape. In one embodiment, the shape of the first surface S 1  may substantially have a first axis and a second axis which are perpendicular to each other. The shape of the fourth surface S 4  may also substantially have a first axis and a second axis which are perpendicular to each other. Although the first surface S 1  and fourth surface S 4  have a first axis and a second axis, this does not mean that the first surface S 1  and fourth surface S 4  need to be completely symmetrical. The first surface S 1  and fourth surface S 4  may only have a substantially corresponding shape. The wires or metal line may be omitted. The deviation resulted from the manufacture variation may also be omitted. In some embodiments of the present disclosure, when the length of the first axis and the length of the second axis are the same, the first surface S 1  and the fourth surface S 4  may have a symmetrical shape. For example, the first surface S 1  and the fourth surface S 4  may have a circular shape or a square shape. In other embodiments of the present disclosure, when the length of the first axis and the length of the second axis are different, the first surface S 1  and the fourth surface S 4  may have a non-symmetrical shape. For example, the first surface S 1  and the fourth surface S 4  may have an oval shape or a rectangular shape. In this embodiment, if the length of the first axis is greater than the length of the second axis, the first axis may also be referred to as the major axis, and the second axis may also be referred to as the minor axis. In addition, in some embodiments of the present disclosure, the shape of the first surface S 1  and the shape of the fourth surface S 4  may be the same. However, in other embodiments of the present disclosure, the shape of the first surface S 1  and the shape of the fourth surface S 4  may be different. 
     The relationship between the specific width, the distance, the ratio of the stack structure and the half width at half maximum when the first surface S 1  and the fourth surface S 4  have various shapes is described as follows.  FIG. 4A  is a schematic view of the stack structure  112  in accordance with some embodiments of the present disclosure. As shown in  FIG. 4A , in some embodiments of the present disclosure, the distance of the first axis D 1 A of the first surface S 1  is the same as the distance of the second axis D 1 B of the first surface S 1  (both are the width D 1 ). In addition, the distance of the first axis D 3 A of the fourth surface S 4  is the same as the distance of the second axis D 3 B of the fourth surface S 4  (both are the width D 3 ). The first surface S 1  and the fourth surface S 4  have a circular shape. The relationship between the distance H 1 , the distance H 2 , the width D 1 , the width D 2 , the width D 3 , the angle θ(for example, the second angle θ 2  and the first angle θ 1 ), the specific ratio R and the half width at half maximum of   the emitted light of the light-emitting diode  104  and the light-emitting effectiveness is shown in the following Table 1. In addition, although the first surface S 1  and the fourth surface S 4  have a first axis and a second axis, this does not mean that the first surface S 1  and fourth surface S 4  need to be completely symmetrical. The first surface S 1  and fourth surface S 4  may only have a substantially corresponding shape. The wires or metal line may be omitted. The deviation resulted from the manufacture variation may also be omitted. In table 1, the unit of width and length is um. In addition, in this embodiment, the stack structure  112  has a first sidewall  112 S 1  and a second sidewall  112 S 2  which are opposite to each other. And the size of the light-emitting opening of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . The direction perpendicular to the first surface S 1  and the fourth surface S 4  is the direction A 1 . The acute angle between the first sidewall  112 S 1  of the stack structure  112  and the direction A 1  is the first angle θ 1 , the acute angle between the second sidewall  112 S 2  of the stack structure  112  and the direction A 1  is the second angle θ 2 . In this embodiment, as shown in  FIG. 4A , the second angle θ 2  and the first angle θ 1  are the same. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 1 
               
               
                   
               
               
                 H1 (um) 
                 H2 (um) 
                 D3 (um) 
                 D1 (um) 
                 θ1 = θ2 
                 D2 (um) 
                 R 
                 Light-emitting effectiveness 
                 HWHM 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 6 
                 1 
                 1 
                 0° 
                 1 
                 0.857 
                 2.95 lm 
                  5.9% 
                 50° 
               
               
                   
                   
                   
                 2 
                 4.09° 
                 1.14 
                 0.490 
                 12.23 lm 
                 24.5% 
                 60° 
               
               
                   
                   
                   
                 3 
                 8.13° 
                 1.29 
                 0.367 
                 25.55 lm 
                 51.1% 
                 60° 
               
               
                   
                   
                   
                 4 
                 12.09° 
                 1.43 
                 0.306 
                 30.20 lm 
                 60.4% 
                 45° 
               
               
                   
                   
                   
                 5 
                 15.95° 
                 1.57 
                 0.269 
                 31.63 lm 
                 63.3% 
                 33° 
               
               
                 6 
                 5 
                 1 
                 1 
                 0° 
                 1 
                 0.833 
                 3.06 lm 
                  6.1% 
                 50° 
               
               
                   
                   
                   
                 2 
                 4.76° 
                 1.17 
                 0.486 
                 12.65 lm 
                 25.3% 
                 60° 
               
               
                   
                   
                   
                 3 
                 9.46° 
                 1.33 
                 0.370 
                 25.64 lm 
                 51.3% 
                 60° 
               
               
                   
                   
                   
                 4 
                 14.04° 
                 1.50 
                 0.313 
                 29.85 lm 
                 59.7% 
                 45° 
               
               
                   
                   
                   
                 5 
                 18.43° 
                 1.67 
                 0.278 
                 31.01 lm 
                   62% 
                 33° 
               
               
                 5 
                 4 
                 1 
                 1 
                 0° 
                 1 
                 0.8 
                 3.17 lm 
                  6.3% 
                 50° 
               
               
                   
                   
                   
                 2 
                 5.71° 
                 1.2 
                 0.48 
                 12.98 lm 
                   26% 
                 60° 
               
               
                   
                   
                   
                 3 
                 11.31° 
                 1.4 
                 0.373 
                 25.52 lm 
                   51% 
                 60° 
               
               
                   
                   
                   
                 4 
                 16.7° 
                 1.6 
                 0.32 
                 29.58 lm 
                 59.2% 
                 45° 
               
               
                   
                   
                   
                 5 
                 21.8° 
                 1.8 
                 0.288 
                 30.67 lm 
                 61.3% 
                 40° 
               
               
                 4 
                 3 
                 1 
                 1 
                 0° 
                 1 
                 0.75 
                 3.3 lm 
                  6.6% 
                 50° 
               
               
                   
                   
                   
                 2 
                 7.13° 
                 1.25 
                 0.469 
                 13.5 lm 
                   27% 
                 60° 
               
               
                   
                   
                   
                 3 
                 14.04° 
                 1.5 
                 0.375 
                 24.96 lm 
                 49.9% 
                 60° 
               
               
                   
                   
                   
                 4 
                 20.56° 
                 1.75 
                 0.328 
                 27.64 lm 
                 55.3% 
                 45° 
               
               
                   
                   
                   
                 5 
                 26.57° 
                 2 
                 0.3 
                 28.67 lm 
                 57.3% 
                 45° 
               
               
                 3 
                 2 
                 1 
                 1 
                 0° 
                 1 
                 0.667 
                 3.44 lm 
                  6.9% 
                 50° 
               
               
                   
                   
                   
                 2 
                 9.46° 
                 1.33 
                 0.444 
                 13.93 lm 
                 27.9% 
                 60° 
               
               
                   
                   
                   
                 3 
                 18.43° 
                 1.67 
                 0.37 
                 23.81 lm 
                 47.6% 
                 55° 
               
               
                   
                   
                   
                 4 
                 26.57° 
                 2 
                 0.333 
                 26.39 lm 
                 52.8% 
                 45° 
               
               
                   
                   
                   
                 5 
                 33.69° 
                 2.33 
                 0.311 
                 29.79 lm 
                 59.6% 
                 60° 
               
               
                   
               
            
           
         
       
     
     In addition,  FIG. 4B  is an analytical figure of the width D 1  of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure, which corresponds to the data shown in Table 1. In this embodiment, the ratio R may range from about 0.269 to 0.857 (0.269≦R≦0.857). In addition,  FIG. 4C  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.269 and is less than 0.3. In  FIG. 4C , the half width at half maximum is ±30°. In addition,  FIG. 4D  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.3 and is less than 0.328. In  FIG. 4D , the half width at half maximum is ±40°. In addition,  FIG. 4E  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.328 and is less than 0.375. In  FIG. 4E , the half width at half maximum is ±60°. In addition,  FIG. 4F  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.375 and is less than 0.49. In  FIG. 4F , the half width at half maximum is ±60°. In addition,  FIG. 4G  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.49 and is less than 0.857. In  FIG. 4G , the half width at half maximum is ±50°. In addition, in the above figures, the solid line represents the distribution figure of the emitted light at various view angles along the direction of the first axis, and the dash line represents the distribution figure of the emitted light at various view angles along the direction of the second axis. Since the length of the first axis is the same as the length of the second axis in this embodiment, the solid line substantially overlaps with the dash line. 
     Therefore, by tuning the ratio R which ranges from about 0.269 to 0.857, the light-emitting diode display device of some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely. 
     In addition, when the distance H 1  is 3 μm, the half width at half maximum in  FIG. 4B  increases. This is because the height of the stack structure  112  becomes too small when the distance H 1  is 3 μm, and most light is emitted from the stack structure  112  without being reflected by the sidewall of the stack structure  112 . Since most light is not reflected and focused by reflection by the sidewall of the stack structure  112 , the half width at half maximum increases. Therefore, the lower limit of the distance H 1  in  FIG. 4B  is 3 μm. 
       FIG. 5A  is a schematic view of the stack structure  112  in accordance with some embodiments of the present disclosure. As shown in  FIG. 5A , in some embodiments of the present disclosure, the distance of the first axis D 1 A (also referred to as the major axis D 1 A) of the first surface S 1  is greater than the distance of the second axis D 1 B (also referred to as the minor axis D 1 B). In addition, the distance of the first axis D 3 A (also referred to as the major axis D 3 A) of the fourth surface S 4  is greater than the distance of the second axis D 3 B (also referred to as the minor axis D 3 B). The first surface S 1  and the fourth surface S 4  have an oval shape. The relationship between the distance H 1 , the distance H 2 , the distance D 3 A′ of the major axis D 3 A, the distance D 3 B′ of the minor axis D 3 B, the distance D 1 A′ of the major axis D 1 A, the distance D 1 B′ of the minor axis D 1 B and the light-emitting effectiveness of the light-emitting diode  104 , the half width at half maximum A of the emitted light along the direction of the major axis and the half width at half maximum B of the emitted light along the direction of the minor axis is shown in the following Table 2. In addition, although the first surface S 1  and fourth surface S 4  have the first axis and the second axis, this does not mean that the first surface S 1  and fourth surface S 4  need to be completely symmetrical. The first surface S 1  and fourth surface S 4  may only have a substantially corresponding shape. The wires or metal line may be omitted. The deviation resulted from the manufacture variation may also be omitted. In addition, in this embodiment, the stack structure  112  has a first sidewall  112 S 1  and a second sidewall  112 S 2  which are opposite to each other. And the size of the light-emitting opening  117  of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . The direction perpendicular to the first surface S 1  and the fourth surface S 4  is the direction A 1 . The acute angle between the first sidewall  112 S 1  of the stack structure  112  and the direction A 1  is the first angle θ 1 , the acute angle between the second sidewall  112 S 2  of the stack structure  112  and the direction A 1  is the second angle θ 2 . In this embodiment, as shown in  FIG. 5A , the second angle θ 2  and the first angle θ 1  are the same. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 2 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 Light-emitting 
                   
                   
               
               
                 H1 (um) 
                 H2 (um) 
                 D3A′ (um) 
                 D3B′ (um) 
                 D1A′ (um) 
                 D1B′ (um) 
                 effectiveness 
                 HWHM A 
                 HWHM B 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 6 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.61 lm 
                 0.052% 
                 35° 
                 35° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 10.34 lm 
                 0.207% 
                 50° 
                 50° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.04 lm 
                 0.441% 
                 55° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 27.35 lm 
                 0.547% 
                 45° 
                 48° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 29.26 lm 
                 0.585% 
                 38° 
                 35° 
               
               
                 6 
                 5 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.78 lm 
                 0.056% 
                 40° 
                 40° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 10.85 lm 
                 0.217% 
                 55° 
                 55° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.49 lm 
                 0.450% 
                 55° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 27.38 lm 
                 0.548% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 29.13 lm 
                 0.583% 
                 40° 
                 35° 
               
               
                 5 
                 4 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.99 lm 
                 0.060% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 11.34 lm 
                 0.227% 
                 55° 
                 55° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.34 lm 
                 0.447% 
                 55° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 26.74 lm 
                 0.535% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 28.10 lm 
                 0.562% 
                 40° 
                 35° 
               
               
                 4 
                 3 
                 1 
                 0.5 
                 1 
                 0.50 
                 3.23 lm 
                 0.065% 
                 50° 
                 50° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 11.91 lm 
                 0.238% 
                 60° 
                 60° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 21.74 lm 
                 0.435% 
                 55° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 25.94 lm 
                 0.519% 
                 50° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 26.92 lm 
                 0.538% 
                 45° 
                 40° 
               
               
                 3 
                 2 
                 1 
                 0.5 
                 1 
                 0.50 
                 3.58 lm 
                 0.072% 
                 55° 
                 55° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 12.31 lm 
                 0.246% 
                 65° 
                 65° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 21.18 lm 
                 0.424% 
                 55° 
                 65° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 24.46 lm 
                 0.489% 
                 50° 
                 50° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 25.25 lm 
                 0.505% 
                 50° 
                 40° 
               
               
                   
               
            
           
         
       
     
     In addition,  FIG. 5B  is an analytical figure of the distance MA of the major axis of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure.  FIG. 5C  is an analytical figure of the distance D 1 B of the minor axis of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure. The results shown in  FIG. 5B  and  FIG. 5C  correspond to the data shown in Table 2. 
     Referring to  FIGS. 5D-5H , the solid line in  FIGS. 5D-5H  represents the distribution figure of the emitted light at various view angles along the direction of the major axis, and the dash line in  FIGS. 5D-5H  represents the distribution figure of the emitted light at various view angles along the direction of the minor axis.  FIG. 5D  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis MA of the first surface S 1  is 1 μm, the distance of the minor axis D 1 B of the first surface S 1  is 0.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     In addition,  FIG. 5E  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis MA of the first surface S 1  is 2 μm, the distance of the minor axis D 1 B of the first surface S 1  is 1 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
       FIG. 5F  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 3 μm, the distance of the minor axis D 1 B of the first surface S 1  is 1.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
       FIG. 5G  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 4 μm, the distance of the minor axis D 1 B of the first surface S 1  is 2 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
       FIG. 5H  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 5 μm, the distance of the minor axis D 1 B of the first surface S 1  is 2.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     Therefore, by tuning the distance of the major axis of the first surface and the distance of the minor axis of the first surface, the light-emitting diode display device of some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely. 
       FIG. 6A  is a schematic view of the stack structure  112  in accordance with some embodiments of the present disclosure. As shown in  FIG. 6A , in some embodiments of the present disclosure, the distance of the first axis D 1 A of the first surface S 1  is the same as the distance of the second axis D 1 B of the first surface S 1  (both are the width D 1 ). In addition, the distance of the first axis D 3 A of the fourth surface S 4  is the same as the distance of the second axis D 3 B of the fourth surface S 4  (both are the width D 3 ). The first surface S 1  and the fourth surface S 4  have a square shape. The relationship between the distance H 1 , the distance H 2 , the width D 1 , the width D 2 , the width D 3 , the angle θ(for example, the second angle θ 2  and the first angle θ 1 ), the specific ratio R and the half width at half maximum of the emitted light of the light-emitting diode  104  and the light-emitting effectiveness is shown in the following Table 3. In addition, although the first surface S 1  and fourth surface S 4  have a first axis and a second axis, this does not mean that the first surface S 1  and fourth surface S 4  need to be completely symmetrical. The first surface S 1  and fourth surface S 4  may only have a substantially corresponding shape. The wires or metal line may be omitted. The deviation resulted from the manufacture variation may also be omitted. In addition, in this embodiment, the stack structure  112  has a first sidewall  112 S 1  and a second sidewall  112 S 2  which are opposite to each other. And the size of the light-emitting opening  117  of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . The direction perpendicular to the first surface S 1  and the fourth surface S 4  is the direction A 1 . The acute angle between the first sidewall  112 S 1  of the stack structure  112  and the direction A 1  is the first angle θ 1 , the acute angle between the second sidewall  112 S 2  of the stack structure  112  and the direction A 1  is the second angle θ 2 . In this embodiment, as shown in  FIG. 6A , the second angle θ 2  and the first angle θ 1  are the same. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 3 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                   
                 Light-emitting 
                   
               
               
                 H1 (um) 
                 H2 (um) 
                 D3 (um) 
                 D1 (um) 
                 θ1 = θ2 
                 D2 (um) 
                 R 
                 effectiveness 
                 HWHM 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 6 
                 1 
                 1 
                 0.00° 
                 1.00 
                 0.857 
                 2.94 lm 
                 5.87% 
                 50° 
               
               
                   
                   
                   
                 2 
                 4.09° 
                 1.14 
                 0.490 
                 12.17 lm 
                 24.35% 
                 60° 
               
               
                   
                   
                   
                 3 
                 8.13° 
                 1.29 
                 0.367 
                 24.59 lm 
                 49.17% 
                 60° 
               
               
                   
                   
                   
                 4 
                 12.09° 
                 1.43 
                 0.306 
                 28.43 lm 
                 56.87% 
                 45° 
               
               
                   
                   
                   
                 5 
                 15.95° 
                 1.57 
                 0.269 
                 29.41 lm 
                 58.82% 
                 35° 
               
               
                 6 
                 5 
                 1 
                 1 
                 0.00° 
                 1.00 
                 0.833 
                 3.04 lm 
                 6.08% 
                 50° 
               
               
                   
                   
                   
                 2 
                 4.76° 
                 1.17 
                 0.486 
                 12.62 lm 
                 25.24% 
                 60° 
               
               
                   
                   
                   
                 3 
                 9.46° 
                 1.33 
                 0.370 
                 24.46 lm 
                 48.92% 
                 60° 
               
               
                   
                   
                   
                 4 
                 14.04° 
                 1.50 
                 0.313 
                 27.72 lm 
                 55.45% 
                 45° 
               
               
                   
                   
                   
                 5 
                 18.43° 
                 1.67 
                 0.278 
                 28.40 lm 
                 56.80% 
                 35° 
               
               
                 5 
                 4 
                 1 
                 1 
                 0.00° 
                 1.00 
                 0.800 
                 3.17 lm 
                 6.34% 
                 50° 
               
               
                   
                   
                   
                 2 
                 5.71° 
                 1.20 
                 0.480 
                 12.95 lm 
                 25.90% 
                 60° 
               
               
                   
                   
                   
                 3 
                 11.31° 
                 1.40 
                 0.373 
                 24.02 lm 
                 48.03% 
                 60° 
               
               
                   
                   
                   
                 4 
                 16.70° 
                 1.60 
                 0.320 
                 26.96 lm 
                 53.91% 
                 45° 
               
               
                   
                   
                   
                 5 
                 21.80° 
                 1.80 
                 0.288 
                 27.14 lm 
                 54.27% 
                 40° 
               
               
                 4 
                 3 
                 1 
                 1 
                 0.00° 
                 1.00 
                 0.750 
                 3.29 lm 
                 6.58% 
                 50° 
               
               
                   
                   
                   
                 2 
                 7.13° 
                 1.25 
                 0.469 
                 13.54 lm 
                 27.08% 
                 60° 
               
               
                   
                   
                   
                 3 
                 14.04° 
                 1.50 
                 0.375 
                 23.18 lm 
                 46.36% 
                 60° 
               
               
                   
                   
                   
                 4 
                 20.56° 
                 1.75 
                 0.328 
                 25.34 lm 
                 50.67% 
                 45° 
               
               
                   
                   
                   
                 5 
                 26.57° 
                 2.00 
                 0.300 
                 25.18 lm 
                 50.36% 
                 45° 
               
               
                 3 
                 2 
                 1 
                 1 
                 0.00° 
                 1.00 
                 0.667 
                 3.44 lm 
                 6.88% 
                 50° 
               
               
                   
                   
                   
                 2 
                 9.46° 
                 1.33 
                 0.444 
                 13.78 lm 
                 27.57% 
                 60° 
               
               
                   
                   
                   
                 3 
                 18.43° 
                 1.67 
                 0.370 
                 22.38 lm 
                 44.77% 
                 50° 
               
               
                   
                   
                   
                 4 
                 26.57° 
                 2.00 
                 0.333 
                 23.92 lm 
                 47.83% 
                 50° 
               
               
                   
                   
                   
                 5 
                 33.69° 
                 2.33 
                 0.311 
                 27.81 lm 
                 55.61% 
                 60° 
               
               
                   
               
            
           
         
       
     
     In addition,  FIG. 6B  is an analytical figure of the width D 1  of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure, which corresponds to the data shown in Table 3. In this embodiment, the ratio R may range from about 0.269 to 0.857 (0.269≦R≦0.857). In addition,  FIG. 6C  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.269 and is less than 0.3. In  FIG. 6C , the half width at half maximum is ±30°. In addition,  FIG. 6D  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.3 and is less than 0.328. In  FIG. 6D , the half width at half maximum is ±40°. In addition,  FIG. 6E  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.328 and is less than 0.375. In  FIG. 6E , the half width at half maximum is ±60°. In addition,  FIG. 6F  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.375 and is less than 0.49. In  FIG. 6F , the half width at half maximum is ±60°. In addition,  FIG. 6G  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the ratio R is greater than or equal to 0.49 and is less than 0.857. In  FIG. 6G , the half width at half maximum is ±50°. 
     In addition, in the above figures, the solid line represents the distribution figure of the emitted light at various view angles along the direction of the first axis, and the dash line represents the distribution figure of the emitted light at various view angles along the direction of the second axis. Since the length of the first axis is the same as the length of the second axis in this embodiment, the solid line substantially overlaps with the dash line. 
     Therefore, by tuning the ratio R which ranges from about 0.269 to 0.857, the light-emitting diode display device of some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely. 
       FIG. 7A  is a schematic view of the stack structure  112  in accordance with some embodiments of the present disclosure. As shown in  FIG. 7A , in some embodiments of the present disclosure, the distance of the first axis D 1 A (also referred to as the major axis D 1 A) of the first surface S 1  is greater than the distance of the second axis D 1 B (also referred to as the minor axis D 1 B). In addition, the distance of the first axis D 3 A (also referred to as the major axis D 3 A) of the fourth surface S 4  is greater than the distance of the second axis D 3 B (also referred to as the minor axis D 3 B). The first surface S 1  and the fourth surface S 4  have a rectangular shape. The relationship between the distance H 1 , the distance H 2 , the distance D 3 A′ of the major axis D 3 A, the distance D 3 B′ of the minor axis D 3 B, the distance D 1 A′ of the major axis D 1 A, the distance D 1 B′ of the minor axis D 1 B and the light-emitting effectiveness of the light-emitting diode  104 , the half width at half maximum A of the emitted light along the direction of the major axis and the half width at half maximum B of the emitted light along the direction of the minor axis is shown in the following Table 4. In addition, although the first surface S 1  and fourth surface S 4  have the first axis and the second axis, this does not mean that the first surface S 1  and fourth surface S 4  need to be completely symmetrical. The first surface S 1  and fourth surface S 4  may only have a substantially corresponding shape. The wires or metal line may be omitted. The deviation resulted from the manufacture variation may also be omitted. In addition, in this embodiment, the stack structure  112  has a first sidewall  112 S 1  and a second sidewall  112 S 2  which are opposite to each other. And the size of the light-emitting opening  117  of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . The direction perpendicular to the first surface S 1  and the fourth surface S 4  is the direction A 1 . The acute angle between the first sidewall  112 S 1  of the stack structure  112  and the direction A 1  is the first angle θ 1 , the acute angle between the second sidewall  112 S 2  of the stack structure  112  and the direction A 1  is the second angle θ 2 . In this embodiment, as shown in  FIG. 7A , the second angle θ 2  and the first angle θ 1  are the same. 
     
       
         
           
               
               
               
               
               
               
               
               
               
             
               
                 TABLE 4 
               
               
                   
               
               
                   
                   
                   
                   
                   
                   
                 Light-emitting 
                 HWHM 
                 HWHM 
               
               
                 H1 (um) 
                 H2 (um) 
                 D3A′ (um) 
                 D3B′ (um) 
                 D1A′ (um) 
                 D1B′ (um) 
                 effectiveness 
                 A 
                 B 
               
               
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
               
               
               
               
               
            
               
                 7 
                 6 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.60 lm 
                 5.20% 
                 50° 
                 40° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 10.36 lm 
                 20.72% 
                 60° 
                 50° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.05 lm 
                 44.11% 
                 58° 
                 580 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 26.78 lm 
                 53.56% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 28.70 lm 
                 57.40% 
                 35° 
                 30° 
               
               
                 6 
                 5 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.74 lm 
                 5.49% 
                 50° 
                 45° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 10.80 lm 
                 21.60% 
                 60° 
                 50° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.31 lm 
                 44.62% 
                 60° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 26.65 lm 
                 53.31% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 28.22 lm 
                 56.44% 
                 35° 
                 35° 
               
               
                 5 
                 4 
                 1 
                 0.5 
                 1 
                 0.50 
                 2.89 lm 
                 5.79% 
                 50° 
                 40° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 11.21 lm 
                 22.42% 
                 60° 
                 50° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 22.19 lm 
                 44.38% 
                 60° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 26.30 lm 
                 52.59% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 27.47 lm 
                 54.95% 
                 45° 
                 35° 
               
               
                 4 
                 3 
                 1 
                 0.5 
                 1 
                 0.50 
                 3.05 lm 
                 6.11% 
                 60° 
                 45° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 11.69 lm 
                 23.37% 
                 60° 
                 50° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 21.59 lm 
                 43.17% 
                 60° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 25.21 lm 
                 50.42% 
                 45° 
                 45° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 25.70 lm 
                 51.40% 
                 45° 
                 40° 
               
               
                 3 
                 2 
                 1 
                 0.5 
                 1 
                 0.50 
                 3.24 lm 
                 6.48% 
                 55° 
                 50° 
               
               
                   
                   
                   
                   
                 2 
                 1.00 
                 11.98 lm 
                 23.97% 
                 60° 
                 65° 
               
               
                   
                   
                   
                   
                 3 
                 1.50 
                 20.83 lm 
                 41.66% 
                 50° 
                 60° 
               
               
                   
                   
                   
                   
                 4 
                 2.00 
                 23.52 lm 
                 47.04% 
                 50° 
                 50° 
               
               
                   
                   
                   
                   
                 5 
                 2.50 
                 25.78 lm 
                 51.56% 
                 60° 
                 45° 
               
               
                   
               
            
           
         
       
     
     In addition,  FIG. 7B  is an analytical figure of the distance MA of the major axis of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure.  FIG. 7C  is an analytical figure of the distance D 1 B of the minor axis of the first surface S 1  of the stack structure  112  (or the bottom surface of the stack structure  112 ) versus the half width at half maximum in accordance with this embodiment of the present disclosure. The results shown in  FIG. 7B  and  FIG. 7C  correspond to the data shown in Table 4. 
       FIG. 7D  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 1 μm, the distance of the minor axis D 1 B of the first surface S 1  is 0.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     In addition,  FIG. 7E  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis MA of the first surface S 1  is 2 μm, the distance of the minor axis D 1 B of the first surface S 1  is 1 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     In addition,  FIG. 7F  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 3 μm, the distance of the minor axis D 1 B of the first surface S 1  is 1.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     In addition,  FIG. 7G  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 4 μm, the distance of the minor axis D 1 B of the first surface S 1  is 2 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
       FIG. 7H  is a distribution figure of the emitted light at various view angles in accordance with this embodiment of the present disclosure when the distance of the major axis D 1 A of the first surface S 1  is 5 μm, the distance of the minor axis D 1 B of the first surface S 1  is 2.5 μm, the distance of the major axis D 3 A of the fourth surface S 4  is 1 μm, the distance of the minor axis D 3 B of the fourth surface S 4  is 0.5 μm, the distance H 1  is 7 μm and the distance H 2  is 6 μm. 
     In addition, the solid line in  FIGS. 5D-5H  represents the distribution figure of the emitted light at various view angles along the direction of the major axis, and the dash line in  FIGS. 5D-5H  represents the distribution figure of the emitted light at various view angles along the direction of the minor axis. 
     Therefore, by tuning the distance of the major axis of the first surface and the distance of the minor axis of the first surface, the light-emitting diode display device of some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely. 
       FIG. 8A  is a cross-sectional view of the stack structure  112  in accordance with some embodiments of the present disclosure. The light L is the light emitted from the light-emitting layer  108 . The direction perpendicular to the first surface S 1  and the fourth surface S 4  is the direction A 1 , and the direction perpendicular to the first sidewall  112 S 1  of the stack structure  112  is the direction A 2 . The shape of the first surface S 1  and the fourth surface S 4  when viewed from a top view may be the shape shown in  FIGS. 4A, 5A, 6A, 7A  or any other suitable shape. In addition, in this embodiment, the size of the light-emitting opening  117  of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . 
     In the stack structure  112 , the acute angle between the light L just emitted from the light-emitting layer  108  and the direction A 1  at the light-emitting layer  108  is θ e , the acute angle between the light L and the direction A 2  at the first sidewall  112 S 1  is θ r , the acute angle between the light L reflected by the sidewall  112 S 1  of the stack structure  112  and the direction A 1  at the first surface S 1  is 9 In addition, the acute angle between the light L emitted from the stack structure  112  and the direction A 1  at the first surface S 1  is θ o . Since the thickness of the light-emitting layer is thinner than that of other layers, the thickness of the light-emitting layer is omitted in the embodiments of the present disclosure. 
     In addition, when viewed from a cross-sectional view, the acute angle between the direction A 1  and the first sidewall  112 S 1  of the stack structure  112  is the first angle θ 1 . The first angle θ 1  may range from about 1 to 89 degrees. In addition, the stack structure  112  may further include the second sidewall  112 S 2 , and the first sidewall  112 S 1  and the second sidewall  112 S 2  are opposite to each other. The acute angle between the direction A 1  and the second sidewall  112 S 2  of the stack structure  112  is the second angle θ 2 . In this embodiment, as shown in  FIG. 8A , the second angle θ 2  is the same as the first angle θ 1 . 
     As shown in  FIG. 8A , the angle θ r  is equals 90° minus the angle θ e  and plus the first angle θ 1  (θ r =(90°−θ e )+θ 1 ), and the angle θ i  equals to 90° minus the angle θ r  and plus the first angle θ 1  (θ i =90°−(θ r +θ 1 )). Therefore, the angle θ i  equals the angle θ e  minus two times the first angle θ 1  (θ i =θ e −(2×θ 1 )). If the light L is emitted from the stack structure  112  after n times reflections, the angle θ i  equals the angle θ e  minus 2n times the first angle θ 1  (θ i =θ e −(2n×θ 1 )). 
     In addition, according to Snell&#39;s Law, when n1 is the index of refraction of the bulk portion  106 B (or the first conductive-type semiconductor layer  106 ) and n2 is the index of refraction of the medium that the light L is located at after being emitted from the stack structure  112  (or the bulk portion  106 B), the angle θ o , the angle θ i , the index of refraction n1 and the index of refraction n2 have a relationship expressed by the following equation 2: 
     
       
         
           
             
               
                 
                   
                     θ 
                     o 
                   
                   = 
                   
                     
                       sin 
                       
                         - 
                         1 
                       
                     
                     ⁢ 
                     
                       
                         
                           n 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                           × 
                           sin 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           θ 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           1 
                         
                         
                           n 
                           ⁢ 
                           
                               
                           
                           ⁢ 
                           2 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   2 
                 
               
             
           
         
       
     
     In some embodiments of the present disclosure, the material of the first conductive-type semiconductor layer  106  is GaN, and the index of refraction n1 is 2.38. The medium that the light L is located at after being emitted from the stack structure  112  (or the bulk portion  106 B) is air and the index of refraction n2 is 1. 
       FIG. 8B  is a cross-sectional view of the stack structure  112  in accordance with some embodiments of the present disclosure. In this embodiment, the size of the light-emitting opening of the reflection layer coated on the first sidewall  112 S 1  and the second sidewall  112 S 2  is the first surface S 1 . The shape of the first surface S 1  and the fourth surface S 4  when viewed from a top view may be the shape shown in  FIGS. 4A, 5A, 6A, 7A  or any other suitable shape. As shown in  FIG. 8B , the second angle θ 2  is different from the first angle θ 1 . In addition, when viewed from a cross-sectional view, the extension line of the fourth surface S 4  is the extension line S 4 E, the extension line of the first sidewall  112 S 1  is the extension line  112 S 1 E, the extension line of the second sidewall  112 S 2  is the extension line  112 S 2 E. The intersection point of the extension line S 4 E and the extension line  112 S 1 E is the point A, the intersection point of the extension line S 4 E and the extension line  112 S 2 E is the point D, the intersection point of the first surface S 1  and the extension line  112 S 1 E is the point B, the intersection point of the first surface S 1  and the extension line  112 S 2 E is the point C. In other words, the point B and the point C are two end points of the reflection layer on the first sidewall  112 S 1  and the second sidewall  112 S 2 . Two end points of the light-emitting layer  108  (shown by dash line in  FIG. 8B  in order to clearly describe the embodiments of the present disclosure) are the point E and the point F. In addition, the projected point of the point A along the direction A 1  on the light-emitting layer  108  is the point G, the projected point of the point A along the direction A 1  on the first surface S 1  is the point G′, the projected point of the point D along the direction A 1  on the light-emitting layer  108  is the point H, the projected point of the point D along the direction A 1  on the first surface S 1  is the point H′. In addition, the intersection point of the first surface S 1  and the line which is parallel to the line DC and penetrates through the point A is the point Q. In other words, the line AQ is parallel to the line DC. In addition, the intersection of the line AQ and the light-emitting layer  108  (or the line EF) is the point P. Since the thickness of the light-emitting layer is thinner than that of other layers, the thickness of the light-emitting layer is omitted in the embodiments of the present disclosure. 
     According to  FIG. 8B , the ratio of the length of the line AE to the length of the line AB equals the ratio of the length of the line EP to the length of the line BQ (the length of the line AE:the length of the line AB=the length of the line EP:the length of the line BQ). The length of the line AD is the width D 3 , the length of the line BC is the width D 1 . Accordingly, the ratio of the value derived by minus the distance H 1  by the distance H 2  to the distance H 1  is equal to the ratio of the length of the line EP to the value derived by minus the width D 1  by the width D 3  ((H 1 −H 2 ):H 1 =(the length of the line EP):(D 1 −D 3 )). Accordingly, the length of the line EP may be represented by the following equation 3: 
     
       
         
           
             
               
                 
                   
                     EP 
                     _ 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             H 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             1 
                             × 
                             H 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             2 
                           
                           ) 
                         
                         × 
                         
                           ( 
                           
                             
                               D 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             - 
                             
                               D 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ) 
                         
                       
                       
                         H 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     . 
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   3 
                 
               
             
           
         
       
     
     In addition, according to  FIG. 8B , the length of the line PF is the width D 3 , and the width D 2  of the light-emitting layer  108  equals the length of the line EP plus the length of the line PF. In other words, the width D 2  of the light-emitting layer  108  may be represented by the following equation 4: 
     
       
         
           
             
               
                 
                   
                     D 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     2 
                   
                   = 
                   
                     
                       
                         
                           ( 
                           
                             
                               H 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             - 
                             
                               H 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               2 
                             
                           
                           ) 
                         
                         × 
                         
                           ( 
                           
                             
                               D 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               1 
                             
                             - 
                             
                               D 
                               ⁢ 
                               
                                   
                               
                               ⁢ 
                               3 
                             
                           
                           ) 
                         
                       
                       
                         H 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         1 
                       
                     
                     + 
                     
                       D 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       3. 
                     
                   
                 
               
               
                 
                   equation 
                   ⁢ 
                   
                       
                   
                   ⁢ 
                   4 
                 
               
             
           
         
       
     
     In addition, according to  FIG. 8B , the width D 2  of the light-emitting layer  108  may also be represented by the following equation 5:
 
 D 2= D 3+[( H 1− H 2)×(tan θ1+tan θ2)]  equation 5.
 
     It should be noted that, although the above equations 4 and 5 are used to represent the width D 2  of the light-emitting layer  108  of the stack structure  112  shown in  FIG. 8B  in which the second angle θ 2  is different from the first angle θ 1 , the equations 4 and 5 may also be used to represent the width D 2  of the light-emitting layer  108  of the stack structure  112  shown in  FIG. 8A  in which the second angle θ 2  is the same as the first angle θ 1 . 
       FIG. 9A  is a cross-sectional view of a light-emitting diode  104 A of a display device  200  in accordance with some other embodiments of the present disclosure. Note that the same or similar elements or layers corresponding to those of the semiconductor device are denoted by like reference numerals. The same or similar elements or layers denoted by like reference numerals have the same meaning and will not be repeated for the sake of brevity. 
     The difference between the embodiment shown in  FIG. 9A  and the embodiment shown in  FIG. 1A  is that the reflection layer  116  may include a plurality of sub-reflection layers  116 E which are not electrically connected to each other. The plurality of sub-reflection layers  116 E surrounds the stack structure  112 . In addition, in some embodiments of the present disclosure, as shown in  FIG. 9A , the reflection layer  116  may be in direct contact with the second electrode  114 B. In addition, in some embodiments of the present disclosure, as shown in  FIG. 9A , the sub-reflection layers  116 E disposed over the sidewall  112 S of the bulk portion  106 B of the stack structure  112  are not electrically connected to the sub-reflection layers  116 E disposed over the sidewall of the second conductive-type semiconductor layer  110 . In this embodiment, the reflection layer  116  is substantially disposed over the entire sidewall  112 S of the stack structure  112 . Therefore, the size of the opening  117  along the light-emitting direction is the first surface S 1 , and the first surface S 1  is overlapped with the bottom surface of the stack structure  112 . The shape of the first surface S 1  and the fourth surface S 4  when viewed from a top view may be the shape shown in  FIGS. 4A, 5A, 6A, 7A  or any other suitable shape. 
     In other embodiments of the present disclosure, the size of the opening  117  along the light-emitting direction is the size of the bottom surface of the reflection layer  116  adjacent to the bottom surface of the stack structure  112 . The size of the opening  117  along the light-emitting direction is the first surface S 1 , and the first surface S 1  does not overlap with the bottom surface of the stack structure  112 . In other words, similar to the embodiment shown in  FIG. 1B , when the reflection layer  116  does not completely cover the entire sidewall  112 S of the stack structure  112 , the first surface S 1  is defined by the datum surface formed by the opening  117  of the reflection layer  116  and is substantially parallel to the surface of the substrate portion  106 A. In this embodiment, the first surface S 1  may not coincide with the bottom surface of the bulk portion  106 B. 
       FIG. 9B  is a cross-sectional view of a light-emitting diode  104 B of a display device  300  in accordance with some other embodiments of the present disclosure. The difference between the embodiment shown in  FIG. 9B  and the embodiment shown in  FIG. 9A  is that the reflection layer  116  has a thickness which is gradually changed. In one embodiment, in some embodiments of the present disclosure, the thickness of the reflection layer  116  increases from the first surface S 1  to the fourth surface S 4 . In addition, in some embodiments of the present disclosure, the portion of the reflection layer  116  corresponding to the light-emitting layer  108  may be broken off or spaced apart and may have a spacing  122 . The spacing  122  may not be filled by any material or may be filled by an insulating layer. In addition, in this embodiment, the reflection layer  116  is substantially disposed over the entire sidewall  112 S of the stack structure  112 . Since the opening in the light-emitting direction is the first surface S 1 , the first surface S 1  is overlapped with the bottom surface of the stack structure  112 . The shape of the first surface S 1  and the fourth surface S 4  when viewed from a top view may be the shape shown in  FIGS. 4A, 5A, 6A, 7A  or any other suitable shape. In other embodiments of the present disclosure, the size of the opening along the light-emitting direction is the size of the bottom surface of the reflection layer  116  adjacent to the bottom surface of the stack structure  112 . The size of the opening along the light-emitting direction is the first surface S 1 , and the first surface S 1  does not overlap with the bottom surface of the stack structure  112 . In other words, similar to the embodiment shown in  FIG. 1B , when the reflection layer  116  does not completely cover the entire sidewall  112 S of the stack structure  112 , the first surface S 1  is defined by the datum surface formed by the opening of the reflection layer  116  and is substantially parallel to the surface of the substrate portion  106 A. In this embodiment, the first surface S 1  may not coincide with the bottom surface of the bulk portion  106 B. 
     In addition, in some embodiments of the present disclosure, the sidewall  116 S 1  of the reflection layer  116  may be perpendicular to the first surface S 1 , and the surface  116 S 2  of the reflection layer  116  has a height that is the same as that of the fourth surface S 4 . 
     In some embodiments of the present disclosure, a reflection layer  116  with a thickness which is gradually changed may be formed by the following steps. First, a patterned mask is formed, exposing the region which is predetermined to form the reflection layer  116 . Subsequently, the material of the reflection layer is deposited to form the reflection layer  116 . 
       FIG. 9C  is a cross-sectional view of a light-emitting diode  104 C of a display device  400  in accordance with some other embodiments of the present disclosure. The difference between the embodiment shown in  FIG. 9C  and the embodiment shown in  FIG. 9B  is that the first conductive-type semiconductor layer  106  may further include a plurality of pillar portions  106 C disposed over the substrate portion  106 A. In addition, there is a recess  118  formed by two adjacent pillar portions  106 C of the plurality of pillar portions  106 C and the substrate portion  106 A. In addition, the bulk portion  106 B is disposed in the recess  118 . In addition, in this embodiment, the reflection layer  116  is substantially disposed over the entire sidewall  112 S of the stack structure  112 . Since the opening at the light-emitting direction is the first surface S 1 , the first surface S 1  is overlapped with the bottom surface of the stack structure  112 . The shape of the first surface S 1  and the fourth surface S 4  when viewed from a top view may be the shape shown in  FIGS. 4A, 5A, 6A, 7A  or any other suitable shape. The shapes of the first surface S 1  and the fourth surface S 4  in different stack structures  112  may be different. In other embodiments of the present disclosure, the size of the opening  117  along the light-emitting direction is the size of the bottom surface of the reflection layer  116  adjacent to the bottom surface of the stack structure  112 . The size of the opening along the light-emitting direction is the first surface S 1 , and the first surface S 1  does not overlap with the bottom surface of the stack structure  112 . In other words, similar to the embodiment shown in  FIG. 1B , when the reflection layer  116  does not completely cover the entire sidewall  112 S of the stack structure  112 , the first surface S 1  is defined by the datum surface formed by the opening  117  of the reflection layer  116  and is substantially parallel to the surface of the substrate portion  106 A. In this embodiment, the first surface S 1  may not coincide with the bottom surface of the bulk portion  106 B. 
     In addition, in some embodiments of the present disclosure, a spacing  120  is disposed between the bulk portion  106 B and the sidewall  118 S of the recess  118 . The reflection layer  116  is disposed in the spacing  120 , as shown in  FIG. 9C . In other embodiments of the present disclosure, the spacing  120  is not completely filled by the reflection layer. The spacing  120  may only be partially filled by the reflection layer. As long as the design of the reflection layer may achieve the effect of altering the light shape or improving the light-emitting effectiveness. 
     In addition, in some embodiments of the present disclosure, the portion of the reflection layer  116  corresponding to the light-emitting layer  108  may be broken off or spaced apart and may have a spacing  122 . The spacing  122  may not be filled by any material or may be filled by an insulating layer. 
     In some embodiments of the present disclosure, the light-emitting diode  104 C in  FIG. 9C  may be formed by the following steps. First, the light-emitting diode in  FIG. 9B  is formed. But the first electrode and the second electrode are not formed yet. Subsequently, a first conductive type material is deposited to form a plurality of pillar portions  106 C. Subsequently, the first electrode  114 A, the second electrode  114 B and the reflection layer  116  are formed, and the first electrode  114 A is formed over the pillar portions  106 C. However, in other embodiments of the present disclosure, one or a plurality of etching and deposition steps (used to deposit the light-emitting layer  108 , the second conductive-type semiconductor layer  110  and/or the bulk portion  106 B) may be performed on a first conductive-type semiconductor substrate (not shown) to form spacing  120 , the stack structure  112  and the plurality of pillar portions  106 C. However, it should be noted that the embodiments of the present disclosure is not limited thereto. The light-emitting diode  104 C in  FIG. 9C  may be formed by any other suitable manufacturing method. In addition, in some embodiments of the present disclosure, the substrate portion  106 A, the bulk portion  106 B and the pillar portions  106 C of the first conductive-type semiconductor layer  106  may be formed in one piece. However, in other embodiments of the present disclosure, the substrate portion  106 A and the bulk portion  106 B are formed in one piece, whereas the substrate portion  106 A and the pillar portions  106 C are not formed in one piece. 
     In summary, in some embodiments of the present disclosure, since the specific width and distance in the stack structure of the light-emitting diode have a specific relationship, the light-emitting diode display device in some embodiments of the present disclosure may alter the light-emitting view angle and the light-emitting shape freely. In addition, an additional second lens is not needed in the embodiments of the present disclosure to alter the light-emitting view angle and the light-emitting shape. 
     Note that the above element sizes, element parameters, and element shapes are not limitations of the present disclosure. Those skilled in the art can adjust these settings or values according to different requirements. It should be understood that the display device and method for manufacturing the same of the present disclosure are not limited to the configurations of  FIGS. 1 to 9C . The present disclosure may merely include any one or more features of any one or more embodiments of  FIGS. 1 to 9C . In other words, not all of the features shown in the figures should be implemented in the display device and method for manufacturing the same of the present disclosure. 
     In addition, in some embodiments of the present disclosure, the reflection layer may only be disposed over the sidewall of the bulk portion of the first conductive-type semiconductor layer. The reflection layer  116  may be optionally disposed over the substrate portion of the first conductive-type semiconductor layer. As long as the reflection layer is disposed over at least some regions of the light-emitting path, the light-emitting shape may be altered or the light-emitting effectiveness may be improved. 
     Although some embodiments of the present disclosure and their advantages have been described in detail, it should be understood that various changes, substitutions and alterations can be made herein without departing from the spirit and scope of the disclosure as defined by the appended claims. For example, it will be readily understood by those skilled in the art that many of the features, functions, processes, and materials described herein may be varied while remaining within the scope of the present disclosure. Moreover, the scope of the present application is not intended to be limited to the particular embodiments of the process, machine, manufacture, composition of matter, means, methods and operations described in the specification. As one of ordinary skill in the art will readily appreciate from the disclosure of the present disclosure, processes, machines, manufacture, compositions of matter, means, methods, or operations, presently existing or later to be developed, that perform substantially the same function or achieve substantially the same result as the corresponding embodiments described herein may be utilized according to the present disclosure. Accordingly, the appended claims are intended to include within their scope such processes, machines, manufacture, compositions of matter, means, methods, or operations.