Patent Publication Number: US-2020279983-A1

Title: Light emitting device and method of manufacturing light emitting device

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2019-037669 filed in Japan on Mar. 1, 2019; the entire contents of which are incorporated herein by reference. 
     FIELD 
     Embodiments of the present invention relate to a light emitting device and a method of manufacturing a light emitting device. 
     BACKGROUND 
     A light emitting device that has two transparent insulating substrates and a plurality of LEDs arranged between the insulating substrates is known. A light emitting device of this kind is suitable for a display device that displays a variety of character strings, geometric figures and patterns and so forth, a display lamp and the like. 
     When the above light emitting device is used indoors, sufficient electrical reliability and mechanical reliability can be easily ensured. However, when the light emitting device is used in a harsh outdoor environment or used as a part of an automobile or the like, there is a need to provide a light emitting device that can withstand long-term use in an environment characterized by high temperature and high humidity. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a perspective view of a light emitting device; 
         FIG. 2  is an exploded perspective view of a light emitting device; 
         FIG. 3  is a side view of a light emitting module; 
         FIG. 4  is a plan view of a light emitting device; 
         FIG. 5  is a diagram to show a light emitting element connected to a conductor layer; 
         FIG. 6  is a perspective view of a light emitting element; 
         FIG. 7  is a side view of a flexible cable; 
         FIG. 8  is a diagram for illustrating how to connect a light emitting module and a flexible cable; 
         FIG. 9  is a diagram for illustrating how to manufacture a light emitting module; 
         FIG. 10  is a diagram for illustrating how to manufacture a light emitting module; 
         FIG. 11  is a diagram for illustrating how to manufacture a light emitting module; 
         FIG. 12  is a diagram to show the temperature dependency of tensile storage elastic modulus; 
         FIG. 13  is a diagram to show the temperature dependency of tangent loss; 
         FIG. 14  is a diagram to show the expansion coefficients and water absorption coefficients of samples; 
         FIG. 15  is a diagram to show the relationship between the junction temperature Tj and the number of good samples of light emitting elements; 
         FIG. 16  is a diagram to show results of a thermal cycle test; 
         FIG. 17  is a diagram to show the current-voltage characteristics of light emitting device; 
         FIG. 18  is a diagram to show the current-voltage characteristics of light emitting device; 
         FIG. 19  is a diagram to show a variation of a light emitting module; 
         FIG. 20  is a diagram to show a variation of a light emitting module; 
         FIG. 21  is a diagram to show a variation of a light emitting module; 
         FIG. 22  is a diagram to show an example of the use of a light emitting device; 
         FIG. 23  is a diagram to show a variation of a light emitting device; and 
         FIG. 24  is a diagram to show a variation of a light emitting module. 
     
    
    
     DETAILED DESCRIPTION 
     In order to achieve the above object, according to the present embodiment, a light emitting device has a first insulator, which is transparent to light, a first conductor layer, which is provided on a surface of the first insulator, a second insulator, which is transparent to light and arranged to oppose the first conductor layer, a light emitting element, which is arranged between the first insulator and the second insulator, and connected to the first conductor layer, and a third insulator, which is transparent to light and arranged between the first insulator and the second insulator, and the tensile storage elastic modulus of the third insulator is 1.0×10 9  Pa or greater, up to 1.0×10 10  Pa, at 0° C., and 1.0×10 6  Pa or greater, up to 6.0×10 8  Pa, at 130° C. 
     Now, embodiments of the present invention will be described below with reference to the accompanying drawings. The following description will use an XYZ coordinate system, which consists of an X axis, a Y axis and a Z axis that are orthogonal to each other. 
       FIG. 1  is a perspective view of a light emitting device  10  according to the present embodiment. Also,  FIG. 2  is an exploded perspective view of the light emitting device  10 . As can be seen by referring to  FIGS. 1 and 2 , the light emitting device  10  has a light emitting module  20 , whose longitudinal direction runs along the X-axis direction, a flexible cable  40  that is connected with the light emitting module  20 , a connector  50  that is provided on the flexible cable  40 , and a reinforcing plate  60 . 
       FIG. 3  is a side view of the light emitting module  20 . As shown in  FIG. 3 , the light emitting module  20  has a pair of insulators  21  and  22 , an insulator  24  that is formed between the insulators  21  and  22 , and eight light emitting elements  30   1  to  30   8  that are arranged inside the insulator  24 . The insulators  21  and  22  are film-like members, whose longitudinal direction runs along the X-axis direction. The insulators  21  and  22  are approximately 50 to 300 μm thick, and transparent to visible light. The total luminous transmittance of the insulators  21  and  22  is preferably about 5 to 95%. Note that the total luminous transmittance refers to the total luminous transmittance measured in conformity with the Japanese Industrial Standard JISK7375: 2008. 
     The insulators  21  and  22  are flexible, and their bending modulus of elasticity is 0 kgf/mm 2  or greater, up to 320 kgf/mm 2 . Note that the bending modulus of elasticity is a value that is measured based on a method in conformity with ISO178 (JIS K7171: 2008). As for the materials for the insulators  21  and  22 , polyethylene terephthalate (PET), polyethylene naphthalate (PEN), polycarbonate (PC), polyethylene succinate (PES), cyclic olefin resin (for example, ARTON (registered trademark) by JSR Corporation), acrylic resin and so forth may be used. 
     A conductor layer  23 , approximately 0.05 μm to 10 μm thick, is formed in the lower surface of the insulator  21  (the surface on the −Z-side in  FIG. 3 ) in the above pair of insulators  21  and  22 . The conductor layer  23  is, for example, a vapor-deposited film, a sputtered film, and/or the like. Furthermore, the conductor layer  23  may be a metal film bonded with an adhesive. 
     When the conductor layer  23  is a vapor-deposited film, a sputtered film or the like, the conductor layer  23  is approximately 0.05 to 2 μm thick. When the conductor layer  23  is a bonded metal film, the conductor layer  23  is approximately 2 to 10 μm thick, or approximately 2 to 7 μm thick. In the conductor layer  23 , fine particles of a non-transparent conductive material such as gold, silver, or copper may be attached to the insulator  21  in a mesh pattern. For example, a photosensitive compound of a non-transparent conductive material such as silver halide may be applied to the insulator  21  to form a thin film thereon, and this thin film may be subjected to exposure and development processes to form a conductor layer of a mesh pattern. Furthermore, the conductor layer  23  may be formed by applying a slurry containing fine particles of a non-transparent conductive material such as gold and copper in a mesh pattern by way of screen printing or the like. 
     Furthermore, for example, transparent conductive materials such as indium tin oxide (ITO), fluorine-doped tin oxide (FTO), zinc oxide, indium zinc oxide (IZO) and so forth can be used for the conductor layer  23 . The conductor layer  23  can be formed by, for example, patterning the thin film formed on the insulator  21  by applying laser processing or etching process, based on a sputtering method, an electron beam evaporation method, and so forth. For example, the conductor layer  23  can also be formed by screen-printing a mixture of fine particles of a transparent conductive material, having an average particle diameter of 10 to 300 nm, and a transparent resin binder, on the insulator  21 . Also, the conductor layer  23  can also be formed by forming a thin film made of the above mixture, on the insulator  21 , and patterning this thin film by laser processing or photolithography. 
     The conductor layer  23  is preferably transparent so that the total luminous transmittance specified by JIS K7375 of the light emitting module  20  as a whole is 1% or more. If the total luminous transmittance of the light emitting module  20  as a whole is less than 1%, the light emitting points are no longer recognized as bright points. The transparency of the conductor layer  23  itself varies depending on its structure, but the total luminous transmittance is preferably in the range of 10 to 85%. 
       FIG. 4  is a plan view of the light emitting device  10 . As can be seen by referring to  FIG. 4 , the conductor layer  23  is comprised of an L-shaped conductive circuit  23   a , which is formed along the +Y-side outer edge of the insulator  21 , and rectangular conductive circuits  23   b  to  23   i , which are arranged along the −Y-side outer edge of the insulator  21 . In the light emitting device  10 , the distances D among the conductive circuits  23   a  to  23   i  are preferably 1000 μm or less, more preferably 200 μm or less, and even more preferably 100 μm or less. 
       FIG. 5  is an enlarged view to show a part of the conductive circuits  23   a  and  23   b . As shown in  FIG. 5 , the conductive circuits  23   a  to  23   i  assume a mesh pattern, formed with line patterns where the line width is approximately 5 μm. The line pattern that runs parallel to the X axis is formed roughly at 150-μm intervals, along the Y axis. Also, the line pattern that runs parallel to the Y axis is formed roughly at 150-μm intervals, along the X axis. In each of the conductive circuits  23   a  to  23   i , a pad  23 P, to which the electrodes of the light emitting elements  30   1  to  30   8  are connected, is formed. 
     In the light emitting device  10 , the insulator  22  is shorter than the insulator  21  in the X-axis direction. Consequently, as can be seen by referring to  FIG. 3  and  FIG. 4 , the +X-side ends of the conductive circuit  23   a  and the conductive circuit  23   i  that constitute the conductor layer  23  are exposed. 
     As shown in  FIG. 3 , the insulator  24  is an insulator that is formed between the insulator  21  and the insulator  22 . The insulator  24  is made of, for example, an epoxy thermosetting resin. For example, the minimum melt viscosity VC1 of the insulator  24  before curing is preferably 10 to 10000 Pa·s in a range of 80 to 160° C. Also, the rate of change VR of the minimum melt viscosity VC1 before curing, up to the point where the temperature T1 (minimum softening temperature) is reached, is preferably 1/1000 or less (one thousandth or less). Furthermore, after the insulator  24  reaches the minimum melt viscosity by heating, that is, after curing, its Vicat softening temperature T2 is preferably in the range of 0 to 160° C., and its tensile storage elastic modulus EM in the range of 0 to 100° C. is preferably 0.01 to 1000 GPa. 
     The melt viscosity is a value that is determined by changing the temperature of the measurement object from 50° C. to 180° C., in accordance with the method described in JIS K7233. The Vicat softening temperature is a value that is determined under the conditions of a test load of 10 N and a heating rate of 50° C./hour, in accordance with A50 described in JIS K7206 (ISO 306: 2004). The tensile storage elastic modulus and the loss tangent are values determined based on a method in conformity with JIS K7244-1 (ISO 6721). 
     The tensile storage elastic modulus is measured by carefully polishing both sides of the light emitting module  20  little by little, removing the insulators  21  and  22 , taking out the insulator  24  and using this insulator  24  as the measurement object. The tensile storage elastic modulus of this insulator  24  is a value determined based on a method in conformity with JIS K7244-1 (ISO 6721). 
     The thickness T2 of the insulator  24  is smaller than the height T1 of the light emitting elements  30   1  to  30   8  so as to place the conductor layer  23  and the bumps  37  and  38  in good contact with each other. The insulators  21  and  22  that are in close contact with the insulator  24  have curved shapes so that the parts where the light emitting elements  30   1  to  30   8  are arranged protrude outward and the parts between the light emitting elements  30   1  to  30   8  are depressed. Because the insulators  21  and  22  are bent in this way, the conductor layer  23  is pressed against the bumps  37  and  38  by the insulators  21  and  22 . 
     The thickness T1 of the insulator  24  is 100 to 200 μm, and the thickness T2 is approximately 50 to 150 μm. Also, the thickness T1 of the insulator  24  is preferably 130 to 170 μm, and the thickness T2 is preferably 100 to 140 μm. Note that the thickness T1 is a size that depends on the thickness of the light emitting element  30 . The thickness T1 is substantially equal to the sum of the thickness of the light emitting elements  30  and the thickness of the conductor layer  23 . The thickness of the insulator  24  is in the range of about 40 to 1100 μm. 
     Furthermore, the insulator  24  fills the very small space between the upper surface of the light emitting elements  30   1  to  30   8  and the conductor layer  23 , without a gap, in close contact with the electrodes  35  and  36  and the bumps  37  and  38 . 
     Consequently, the electrical connectivity between the conductor layer  23  and the bumps  37  and  38  and the reliability thereof can be improved. Note that the insulator  24  is made of a light-transmitting or light-shielding material, which has a total luminous transmittance, as defined by JIS K7375, of 0.1% or more. 
     A resin sheet  241  contains thermosetting resins as main components, and becomes the insulator  24  when appropriate processing is performed, which will be described below. In this case, the raw materials of the insulator  24  may include other resin components if necessary. Epoxy resin, thermosetting acrylic resin, styrene resin, ester resin, urethane resin, melamine resin, phenol resin, unsaturated polyester resin, diallyl phthalate resin, urea-formaldehyde resin, alkyd resin, thermosetting polyimide and so forth can be used as thermosetting resin materials. 
     In addition, the resin sheet  241  can use thermoplastic resins as main component or sub-component materials. For the thermoplastic resin materials, polypropylene resin, polyethylene resin, polyvinyl chloride resin, acrylic resin, Teflon resin (registered trademark), polycarbonate resin, acrylonitrile butadiene styrene resin, polyamide resin polyimide resin and so forth can be used. 
     Among these, the epoxy resin shows excellent flowability during softening, adhesion after curing, weather resistance and so forth, in addition to transparency, electrical insulation, flexibility and the like, and therefore is an optimal raw material for a constituent material of the insulator  24 . However, the insulator  24  may be made of resins other than epoxy resin. 
     The light emitting element  30   1  is an LED chip. As shown in  FIG. 6 , the light emitting element  30   1  is an LED chip of a four-layer structure, comprised of a base substrate  31 , an N-type semiconductor layer  32 , an active layer  33 , and a P-type semiconductor layer  34 . 
     The base substrate  31  is a semiconductor substrate made of GaAs, Si, GaP, sapphire and the like. For the base substrate  31 , one that is optically transparent may be used, so that light can be emitted from both upper and lower surfaces of the light emitting element  30 , and from lateral directions. The N-type semiconductor layer  32 , which has the same shape as the base substrate  31 , is formed on the upper surface of the base substrate  31 . Then, the active layer  33  and the P-type semiconductor layer  34  are laminated, in order, on the upper surface of the N-type semiconductor layer  32 . 
     The active layer  33  is made of, for example, InGaN. Also, the P-type semiconductor layer is made of, for example, p-GaN. Note that the light emitting element  30  may have a double hetero (DH) structure or a multiple quantum well (MQW) structure. The active layer  33  and the P-type semiconductor layer  34 , laminated on the N-type semiconductor layer  32 , have a notch formed in the −Y-side and −X-side corner portion, and the surface of the N-type semiconductor layer  32  is exposed through the notch. 
     In the portion of the N-type semiconductor layer  32  that is exposed through the active layer  33  and the P-type semiconductor layer  34 , an electrode  36 , which is electrically connected with the N-type semiconductor layer  32 , is formed. In addition, an electrode  35 , which is electrically connected with the P-type semiconductor layer  34 , is formed in the +X-side and +Y-side corner portion of the P-type semiconductor layer  34 . 
     The electrodes  35  and  36  are made of copper (Cu) and gold (Au), and bumps  37  and  38  are formed on their upper surfaces. The bumps  37  and  38  are made of solder, and shaped like hemispheres. Metal bumps of gold (Au), a gold alloy, and so forth may be used instead of solder bumps. In the light emitting element  30   1 , the bump  37  functions as a cathode electrode, and the bump  38  functions as an anode electrode. 
     Note that only one of the electrodes  35  and  36  of the light emitting element  30 , or both of the electrodes  35  and  36 , may be electrically connected to the conductor layer  23  via the bump  37  or the bump  38 , or the electrodes  35  and  36  may be directly connected to the conductor layer  23  without the bumps  38  and  39 . 
     Also, in the light emitting module  20 , a light emitting element, in which a pair of electrodes  35  and  36  are separately provided on the upper and lower surfaces of the light emitting element, may be used. In that case, the conductor layer  23  is provided also on the surface of the insulator  22 . In this case, bumps may be formed on electrodes connected to the insulator  21 . 
     The light emitting element  30   1  configured as described above is, as shown in  FIG. 5 , arranged between the conductive circuits  23   a  and  23   b , the bump  37  is connected to the pad  23 P of the conductive circuit  23   a , and the bump  38  is connected to the pad  23 P of conductive circuit  23   b.    
     The rest of the light emitting elements  30   2  to  30   8  also have the same configuration as the light emitting element  30   1 . Then, the light emitting element  30   2  is arranged between conductive circuits  23   b  and  23   c , and bumps  37  and  38  are connected to the conductive circuits  23   b  and  23   c , respectively. 
     Following this, in a similar fashion, the light emitting element  30   3  is arranged over conductive circuits  23   c  and  23   d . The light emitting element  30   4  is arranged over conductive circuits  23   d  and  23   e . The light emitting element  30   5  is arranged over conductive circuits  23   e  and  23   f . The light emitting element  30   6  is arranged over conductive circuits  23   f  and  23   g . The light emitting element  30   7  is arranged over conductive circuits  23   g  and  23   h . The light emitting element  30   8  is arranged over conductive circuits  23   h  and  23   i . By this means, the conductive circuits  23   a  to  23   i  and the light emitting elements  30   1  to  30   8  are connected in series. In the light emitting module  20 , the light emitting elements  30   1  to  30   8  are arranged roughly at 10-mm intervals. 
       FIG. 7  is a side view of a flexible cable  40 . As shown in  FIG. 7 , the flexible cable  40  is comprised of a base material  41 , a conductor layer  43  and a cover lay  42 . 
     The base material  41  is a rectangular member, whose longitudinal direction runs along the X-axis direction. This base material  41  is made of polyimide, for example, and a conductor layer  43  is formed on its upper surface. The conductor layer  43  is formed by patterning a copper foil that is stuck on the upper surface of polyimide. In the present embodiment, as shown in  FIG. 4 , the conductor layer  43  is comprised of two conductive circuits  43   a  and  43   b.    
     Referring back to  FIG. 7 , the conductor layer  43 , formed on the upper surface of the base material  41 , is covered with the coverlay  42  that is bonded by vacuum thermo-compression. This coverlay  42  is shorter than the base material  41  in the X-axis direction. Consequently, the −X-side end parts of the circuit patterns  43   a  and  43   b  constituting the conductive circuits  43  are exposed. Also, an opening part  42   a  is provided in the coverlay  42 , and the +X-side end parts of the conductive circuits  43   a  and  43   b  are exposed through this opening part  42   a.    
     As can be seen by referring to  FIG. 4  and  FIG. 8 , the flexible cable  40 , configured as described above, is bonded to the light emitting module  20  in a state in which the conductive circuits  43   a  and  43   b  that are exposed through the coverlay  42  are in contact with the +X-side end parts of the conductive circuits  23   a  and  23   i  of the light emitting module  20 . 
     As shown in  FIG. 2 , a connector  50  is a rectangular-parallelepiped component, and connected to a cable that is routed from a DC power source. The connector  50  is mounted on the upper surface of the +X-side end part of the flexible cable  40 . When the connector  50  is mounted on the flexible cable  40 , as shown in  FIG. 8 , a pair of terminals  50   a  of the connector  50  are connected, respectively, with the conductive circuits  43   a  and  43   b  constituting the conductor layer  43  of the flexible cable  40 , through the opening part  42   a  provided in the coverlay  42 . 
     As shown in  FIG. 2 , the reinforcing plate  60  is a rectangular member, whose longitudinal direction runs along the X-axis direction. The reinforcing plate  60  is made of, for example, epoxy resin or acrylic. This reinforcing plate  60  is, as shown in  FIG. 8 , attached to the lower surface of the flexible cable  40 . Therefore, the flexible cable  40  can be bent between the −X-side end of the reinforcing plate  60  and the +X-side end of the light emitting module  20 . 
     Next, a method of manufacturing the light emitting module  20  constituting the above-described light emitting device  10  will be described. First, as shown in  FIG. 9 , an insulator  21 , which is made of PET, is prepared. Then, a conductor layer  23 , which is comprised of conductive circuits  23   a  to  23   i , is formed on the surface of the insulator  21 . As for the method of forming the conductive circuits  23   a  to  23   i , for example, a subtractive method, an additive method or the like can be used. 
     Next, as shown in  FIG. 10 , a resin sheet  241  is provided on the surface of the insulator  21 , on which the conductive circuits  23   a  to  23   i  are formed. The thickness of this resin sheet  241  is substantially equal to the thickness of the light emitting element  30 , or the thickness of the light emitting element  30  plus bumps  37  and  38 . The resin sheet  241  is made of, for example, thermosetting resins. The resin sheet  241  may contain other resin components and the like if necessary. Advantages of using thermosetting resins include excellent reliability under high temperature and high humidity. 
     Epoxy resin, acrylic resin, styrene resin, ester resin, urethane resin, melamine resin, phenol resin, unsaturated polyester resin, diallyl phthalate resin, urea-formaldehyde resin, alkyd resin, thermosetting polyimide and the like can be used as thermosetting resins. 
     Furthermore, for the resin sheet  241 , materials containing thermoplastic resins as main components can be used. Advantages of using thermoplastic resins include that they are resistant to mechanical shock, show little discoloration under high temperature and high humidity or when irradiated with ultraviolet rays, and are relatively inexpensive. 
     For the thermoplastic materials, polypropylene resin, polyethylene resin, polyvinyl chloride resin, acrylic resin, Teflon resin (registered trademark), polycarbonate resin, acrylonitrile butadiene styrene resin, polyamide resin, polyimide resin and so forth can be used. 
     That is, an appropriate resin sheet is selected depending on the application and environmental conditions. Among these, the epoxy resin shows excellent flowability during softening, adhesion after curing, weather resistance and so forth, in addition to transparency, electrical insulation, flexibility and the like, and therefore is an optimal raw material for a constituent material of the resin sheet  241 . Obviously, the resin sheet  241  may be made of resins other than epoxy resin. 
     Next, the light emitting elements  30   1  to  30   8  are arranged on the resin sheet  241 . At this time, the light emitting elements  30   1  to  30   8  are positioned such that the pads  23 P of the conductive circuits  23   a  to  23   i  are located right below the bumps  37  and  38  of the light emitting element  30 . 
     Next, as shown in  FIG. 11 , the insulator  22  is arranged on the upper surface side of the insulator  21 . 
     Next, the insulators  21  and  22  are each heated and pressed in a vacuum atmosphere. By this means, first, the bumps  37  and  38  formed on the light emitting element  30  penetrate the resin sheet  241 , reach the conductor layer  23 , and are electrically connected to the conductive circuits  23   a  to  23   i . Then, the resin sheet  241 , having been heated and softened, is filled around the light emitting element  30  without a gap, so that the insulator  24  is obtained. In this way, the light emitting module  20  is completed. 
     As shown in  FIG. 8 , the flexible cable  40 , to which the reinforcing plate  60  is attached, is connected to the light emitting module  20  manufactured as described above, and the connector  50  is mounted on this flexible cable  40 , so that the light emitting device  10  shown in  FIG. 1  is completed. With the light emitting device  10 , when a DC voltage is applied to the conductive circuits  43   a  and  43   b  shown in  FIG. 4  via the connector  50 , the light emitting elements  30   1  to  30   8  that constitute the light emitting module  20  emit light. 
     The light emitting module  20  of the light emitting device  10  is structured so that the insulators  21  and  22 , made of PET and/or the like, are bonded by means of the insulator  24 . When the light emitting device  10  is used outdoors or used in a severe environment characterized by high temperature and high humidity, the deterioration over time progresses relatively quickly due to the impact of the temperature and humidity. Consequently, it is necessary to constitute the insulator  24  through an appropriate heating and pressing step, using raw materials that are robust to environments characterized by high temperature and high humidity. 
     In places where the temperature and humidity change a lot, the viscoelasticity of the insulator  24  also varies following changes in temperature. With the light emitting device  10 , electrical coupling is established only between the bumps  37  and  38  of the light emitting elements  30   1  to  30   8  and the pads  23 P of the conductive circuits  23   a  to  23   i , over very small spaces on the order of several tens μm or less. Consequently, when the viscoelasticity of the insulator  24  changes, the electrical contact between the bumps  37  and  38  of the light emitting elements  30   1  to  30   8  held by the insulator  24  and the pads  23 P of the conductive circuits  23   a  to  23   i  may be lost, and the light emitting elements  30   1  to  30   8  may be turned off. Therefore, it is necessary to select optimal resins as resins to constitute the insulator  24 . 
     In addition, with the light emitting device  10 , resins to have characteristics suitable to the environment of use may be used for the insulator  24 . For example, when using the light emitting device  10  in an environment of 85° C., it is preferable that the relationship between the junction temperature Tj of the light emitting elements and the temperature T tan δmax  at which the loss tangent tan δ of the insulator  24  becomes the maximum fulfills the condition represented by the following equation: 
         T   tan δmax &lt;1.65 Tj− 47.5 
     By using a resin with an expansion coefficient less than 21.3% in an environment in which the temperature is 85° C. and the humidity is 40% or greater, up to 85%, as an insulator  24 , a highly reliable light emitting device  10  can be provided. Note that the resin&#39;s expansion coefficient complies with JIS K7197, and is a value measured by using humidity control-type thermomechanical analysis apparatus (TMA) of NETZSCH Japan K.K. 
     Also, while the light emitting elements  30   1  to  30   8  may be approximately 30 to 1000 μm thick, if the light emitting elements  30   1  to  30   8  are 90 to 300 μm thick, the insulator  24  is preferably 90 to 350 μm thick. The linear expansion coefficient of the insulator  24  is preferably 40 ppm/° C. or greater, up to 80 ppm/° C. When polyethylene or polystyrene is used as a material for the insulator  24 , the Young&#39;s modulus is preferably 0.3 to 10 GPa, and, when epoxy is used as a material for the insulator  24 , the Young&#39;s modulus is preferably about 2.4 GPa. 
     The elastic modulus of the insulator  24  is preferably 1900 to 4900 MPa. The haze of the insulator  24  is preferably 15% or less. In addition, b* of the insulator  24  is preferably less than 5. The luminous transmittance of the insulator  24  is preferably 30% or greater. 
     In the event a stress to bend the light emitting device  10  acts on the light emitting device  10  placed in a high-temperature (85° C.) environment, if the bending stress value of the insulator  24  is high, the stability of connection for holding the light emitting elements is ensured. On the other hand, if an excessive stress acts on the light emitting device  10 , the insulator  24  is deformed plastically, and loses its stability of connection. Also, if the bending stress value of the insulator  24  is low, the insulator is easily deformed plastically by the stress, and loses its stability of connection. 
     When the absolute value of the rate of change of the bending stress in a low-temperature environment and the bending stress in a high-temperature environment is large, the stability of connection drops, and this holds not only when a stress acts directly on the light emitting device  10 , but also when a thermal shock applies to the light emitting device  10 , such as when the light emitting device  10  is taken out of a room in which the temperature is low, to outside where the temperature is high, for example. By contrast with this, when the absolute value of the rate of change of the bending stress in a low-temperature environment and the bending stress in a high-temperature environment is small, the stability of connection increases. 
     The thickness of the insulators  21  and  22  is preferably 30 μm or greater, up to 300 μm. Furthermore, the heat-resistant temperature of the insulators  21  and  22  is preferably 100° C. or higher. The elastic modulus is preferably 2000 or greater, up to 4100 MPa. The luminous transmittance is preferably 90% or greater. The thermal conductivity is preferably 0.1 to 0.4 W/m·k. The haze is preferably 2% or less. In addition, b* is preferably less than 2. 
     The thickness of the light emitting elements  30   1  to  30   8  is preferably 30 μm or greater, up to 1000 μm, and the length of one side of the light emitting elements  30   1  to  30   8  is preferably 30 μm or greater, up to 3000 μm. 
     The height of the bumps  37  and  38  of the light emitting elements  30   1  to  30   8  is 30 μm or greater, up to 100 μm before the thermo-compression bonding step in the manufacturing process of the light emitting device  10 . After the thermo-compression bonding step, the height of the bumps  37  and  38  is 10 μm or greater, up to 90 μm. The height and width of the bumps  37  and  38  are preferably 30 μm or greater, up to 100 μm. 
     If the conductor layer  23  is too thick, cracks may be produced in the conductor layer  23  when the light emitting device  10  is bent. On the other hand, if the conductor layer  23  is too thin, the electrical resistance of the conductor layer  23  increases. Therefore, the thickness of the conductor layer  23  is preferably 10 μm or less. 
     Regarding the mesh pattern in which the conductor layer  23  is constituted, if the line width is wide, the transparency is lost. Therefore, the line width of the mesh pattern is preferably 20 μm or less. The luminous transmittance is preferably 50% or greater. On the other hand, regarding the mesh pattern, if the line width is narrow, the electrical resistance increases, which results in increased susceptibility to disconnection. Therefore, the sheet resistance value of the conductor layer  23  is preferably 300Ω/□ or less. 
     In addition, in order to determine what conditions of resin are optimal to provide materials for the insulator  24  constituting light emitting device  10  described above, samples were prepared for an embodiment of the light emitting device  10 , and measured in a variety of ways. Hereinafter, an embodiment of the light emitting device  10  will be described. 
     EXAMPLES 
     To illustrate the present example, light emitting devices  10 A to  10 D were prepared as samples, and a variety of tests were performed. A resin sheet  241  made of an epoxy thermosetting resin A with a relatively high thermosetting temperature was used as the insulator  24  to constitute the light emitting device  10 A. A resin sheet  241  made of an epoxy thermosetting resin B was used as the insulator  24  to constitute the light emitting device  10 B. A resin sheet  241  made of an epoxy thermosetting resin C was used as the insulator  24  to constitute the light emitting device  10 C. A resin sheet  241  made of a polypropylene (PP) thermosetting resin D was used as the insulator  24  to constitute the light emitting device  10 D. 
     Furthermore, a resin sheet  241  made of acrylic thermoplastic resin E was used as the insulator  24  to constitute the light emitting device  10 E for a comparative example. 
     In the heating and pressing process of the insulators  21  and  22  constituting the light emitting devices  10 A to  10 E, the work space where the laminate shown in  FIG. 11  was placed was made a vacuum space with a degree of vacuum of 5 kPa, and pressure was applied while the laminate was heated. The laminate was thermo-compression bonded in the vacuum atmosphere, so that the space between the insulator  21  and the insulator  22  was filled with the softened insulator  24  without a gap. Note that the vacuum atmosphere during the thermo-compression bonding is preferably 5 kPa or less. 
     Also, the insulators  21  and  22  of the light emitting devices  10 A to  10 E were 100 μm thick. The conductor layer  23  was made of copper and was 2 μm thick. The conductive circuits  23   a  to  23   i  assumed a mesh pattern, which was made of a line pattern with a line width of 5 μm and an arrangement pitch of 300 μm. The resin sheet  241  was 120 μm thick. 
     &lt;&lt;Tensile Storage Elastic Modulus/Loss Tangent&gt;&gt; 
     With the present embodiment, a number of samples were prepared for each of the five types of light emitting devices  10 A to  10 E. Then, light emitting devices were randomly selected from a plurality of light emitting devices, and part of the insulators  24  was taken out, and the temperature dependency of the tensile storage elastic modulus, the temperature dependency of loss tangent, and the water absorption coefficients were measured. 
     To be more specific, both sides of the light emitting modules  20  constituting the light emitting devices  10 A to  10 E were polished carefully, thereby removing the insulators  21  and  22 , and taking out the insulators  24 . Next, the insulators  24  that were taken out were cut into a size of 10 mm×50 mm, to prepare test pieces for each of the light emitting devices  10 A to  10 E. Then, using a DMA7100-type dynamic viscoelasticity automatic measuring device manufactured by Hitachi High-Technologies Corporation, the temperature dependency of the tensile storage elastic modulus and loss tangent of the test pieces was measured. 
     The measurement was carried out by increasing the temperature of the test pieces from −75 to 200° C., at a constant rate of 5° C. per minute, and sampling the test pieces at a frequency of 1 Hz.  FIG. 12  is a diagram to show the temperature dependency of the tensile storage elastic modulus. Also,  FIG. 13  is a diagram to show the temperature dependency of loss tangent tan δ. 
     &lt;&lt;Expansion Coefficient&gt;&gt; 
     Similarly, one light emitting device was randomly selected from a plurality of light emitting devices, and the insulator  24  was taken out. Next, the insulators  24  that were taken out were cut into a size of 10 mm×50 mm, to prepare test pieces for each of the light emitting devices  10 A to  10 E. Then, the expansion coefficient of the test pieces when the humidity was increased from 40% to 85% was measured in an environment in which the temperature was 85° C., using a humidity control-type thermomechanical analysis apparatus (TMA) of NETZSCH Japan K.K. 
     &lt;&lt;Water Absorption Coefficient&gt;&gt; 
     Similarly, one light emitting device was randomly selected from a plurality of light emitting devices, and the insulator  24  was taken out. Next, the insulator  24  that was taken out was cut into a size of 10 mm×30 mm, to prepare test pieces for each of the light emitting devices  10 A to  10 E. Then, using a constant temperature and humidity measuring instrument (PL-3J) manufactured by ESPEC CORP, the water absorption coefficient were measured from the weight of each test piece that was sufficiently dry, and the weight of each test piece having been placed in an environment with a temperature of 85° C. and a humidity of 85% for 24 hours. 
       FIG. 14  shows a table to show the expansion coefficient and water absorption coefficient of each sample. Note that, with the light emitting device  10 D, no expansion coefficient could be measured. 
     &lt;&lt;High-Temperature and High-Humidity Test&gt;&gt; 
     Next, the light emitting devices were subjected to a high-temperature and high-humidity test. In the high-temperature and high-humidity test, 24 light emitting devices  10 A were selected out of a plurality of light emitting devices  10 A, and these light emitting devices  10 A were divided into four groups, each consisting of six light emitting devices. Then, the junction temperatures Tj of the light emitting devices  10 A of each group were set to 100° C., 110° C., 120° C., and 130° C., respectively. Next, each light emitting device  10 A was lit for 1000 hours in an environment in which the temperature was 85° C. and the humidity was 85%. When lighting the light emitting device  10 A, each light emitting device  10 A was bent so that the insulator  22  was located on the outside and the radius of curvature was 50 mm. 
     Similarly, for each of the light emitting devices  10 B to  10 E,  24  devices were selected from a plurality of light emitting devices  10 B to  10 E, and these light emitting devices  10 B to  10 E were each divided into four groups, each consisting of six light emitting devices. Then, the junction temperatures Tj of the light emitting devices  10 B to  10 E of each group were set to 100° C., 110° C., 120° C., and 130° C., respectively. Next, each light emitting device  10 A was lit for 1000 hours in an environment in which the temperature was 85° C. and the humidity was 85%. When lighting the light emitting devices  10 B to  10 E, the light emitting devices  10 B to  10 E were all bent so that the insulators  22  were located on the outside and the radius of curvature was 50 mm. 
     As described above, a high-temperature and high-humidity test to light the light emitting devices  10 A to  10 E,  24  each, for 1000 hours was performed, and the number of light emitting devices  10 A to  10 E that kept lighting without problem was checked.  FIG. 15  shows the results of the high-temperature and high-humidity test of each of the light emitting devices  10 A to  10 E. Graphs A3 to E3 show relationships between the numbers of good samples and the junction temperatures of the light emitting devices  10 A to  10 E, respectively. Also, for convenience, the environment in which the temperature is 85° C. and the humidity is 85% is also referred to as the “test environment”. 
     &lt;&lt;Thermal Cycle Test&gt;&gt; 
     Furthermore, the light emitting devices  10 A to  10 E, six of each, were selected and subjected to a thermal cycle test. For the thermal cycle test, the light emitting devices  10 A to  10 E, six each, were provided unlit, and a test, in which 1 minute of exposure in an environment with a temperature of 25° C., 5 minutes of exposure in an environment with a temperature of −40° C., 1 minute of exposure in an environment with a temperature of 25° C., and 1 minute of exposure in an environment with a temperature of 110° C. constitute one cycle, was performed. Then, every time a predetermined cycle was complete, whether each light emitting device was lit was checked.  FIG. 16  is a diagram to show the results of the thermal cycle test. In the table of  FIG. 16 , the denominator shows the number of light emitting devices  10 A to  10 E that were subjected to the test, and the numerator shows the number of good samples (light emitting devices that were lit). 
     Also, upon the thermal cycle test, not only the lighting state was checked per cycle, but also the current-voltage characteristics of the light emitting devices  10  were measured. 
       FIG. 17  is a diagram to show the current-voltage characteristics of the light emitting devices  10 A to  10 D after 1004 cycles in the thermal cycle test. Curves A4 to D4 show the current-voltage characteristics of the light emitting devices  10 A to  10 D, respectively.  FIG. 18  is a diagram to show the current-voltage characteristics of the light emitting device  10 D after 0 to 1004 cycles in the thermal cycle test. Curve DO shows the current-voltage characteristic before the temperature cycle test was started. Curve D42 shows the current-voltage characteristic after 42 cycles. Curve D90 shows the current-voltage characteristic after 90 cycles. Curve D149 shows the current-voltage characteristic after 149 cycles. Curve D890 shows the current-voltage characteristic after 890 cycles. Curve D1004 shows the current-voltage characteristic after 1004 cycles. 
     &lt;&lt;Verification of Measurement Results&gt;&gt; 
     Referring to  FIG. 15  that shows the results of the high-temperature and high-humidity test, all of the light emitting devices  10 A to  10 C ran for 1000 hours, without a failure, even at a junction temperature T j  of 130° C. By contrast with this, with the light emitting devices  10 D, a device was seen to fail at a junction temperature T j  of 130° C. To allow the light emitting devices  10 D to run for 1000 hours without a failure, the temperature of light emitting elements needs to be 120° C. or lower. 
     Also, with the light emitting devices  10 E, devices were seen to fail when the junction temperature T j  was 110° C. To allow the light emitting devices  10 D for 1000 hours without a failure, the temperature of light emitting elements needs to be 100° C. or lower. 
     With the light emitting devices  10 , when a current of a practical value is supplied to the light emitting elements  30   1  to  30   8 , the junction temperature of the light emitting elements  30   1  to  30   8  becomes approximately 110° C. or higher, up to 130° C. When a current smaller than the current corresponding to the junction temperature of 110° C. is supplied, the amount of light from the light emitting elements becomes insufficient. The current corresponding to the junction temperature of 130° C. is greater than the rated current of the light emitting element. 
     Consequently, it is likely that the resin E of the light emitting device  10 E, having a junction temperature below 110° C., is not suitable for the resin sheet  241  to constitute a light emitting device  10 . Furthermore, currents of practical values can be supplied to the light emitting devices  10 A to  10 D having junction temperatures of 110° C. or higher. Therefore, it is likely that the resins A to D constituting the light emitting devices  10 A to  10 D are suitable for light emitting devices  10 , and it is likely that resins A, B and C are particularly suitable for light emitting devices  10 . Given the above, it naturally follows that, in order to fulfill the performance of the light emitting device  10 , the insulator  24  needs to be made of the resins A to D. 
     Curves A1 to E1 shown in  FIG. 12  show the temperature dependency of the tensile storage elastic modulus of the insulators  24 A to  24 E used for the light emitting devices  10 A to  10 E. Also, curves A2 to E2 shown in  FIG. 13  show the temperature dependency of the loss tangent tan δ in the dynamic viscoelasticity of the insulators  24 A to  24 E used for the light emitting devices  10 A to  10 E. 
     As shown in  FIG. 12  and  FIG. 13 , with the insulators  24 A,  24 B,  24 C and  24 D, the tensile storage elastic modulus decreases by about two to three digits before and after the temperature at which the loss tangent tan δ becomes the maximum, but, from the room temperature to the temperature at which the loss tangent tan δ becomes the maximum, the tensile storage elastic modulus is less dependent on temperature. In addition, at and above the temperature at which the loss tangent tan δ becomes the maximum, again, the loss tangent tan δ is less dependent on temperature, and shows the value of 1×10 6  Pa or greater. On the other hand, with the insulator  24 E, the tensile storage elastic modulus keeps decreasing in all regions from −60° C. to 200° C., due to the rise of temperature, and, when 130° C. is reached, the tensile storage elastic modulus shows the value of 1×10 6  Pa or greater. 
     As shown in  FIG. 12 , regarding the insulators  24 A,  24 B,  24 C and  24 D that fulfill the performance of light emitting devices  10 , the tensile storage elastic modulus at 0° C. is 1.0×10 9  Pa or greater, up to 1.0×10 10  Pa, and the tensile storage elastic modulus at 130° C. is 1.0×10 6  Pa or greater, up to 6.0×10 8  Pa. It then follows that the tensile storage elastic modulus of the insulators of the light emitting devices  10  is preferably in the above range. Also, it is more preferable if the tensile storage elastic modulus at 130° C. of the insulators  24 A to  24 D is 2.0×10 6  Pa or greater. Note that the upper limit of the tensile storage elastic modulus may be 6.0×10 8  Pa or greater. 
     The light emitting device  10 A with the insulator  24 A has the highest tensile storage elastic modulus at the maximum junction temperature of the light emitting element, which is about 130° C., and has no problem in both the high temperature and high humidity test and the thermal cycle test. However, although the resin sheet  241  for forming the light emitting device  10 A with the insulator  24 A has high heat resistance after curing, does not discolor even after the test, and is excellent in processability, it is still a special resin and is very expensive. 
     On the other hand, the resin sheets  241 B,  241 C,  241 D, and  241 E are relatively inexpensive general-purpose resins. Among these, the light emitting devices  10 B and  10 C showed results that were comparable to those of the light emitting device  10 A in the high temperature and high humidity test and the thermal cycle test. 
     Considering the above results, with the insulator  24 , the tensile storage elastic modulus at about 130° C. should be 6×10 8  Pa or less, preferably 2×10 8  Pa or less. 
     As shown in  FIG. 13 , the temperature at which the loss tangent tan δ becomes the maximum in the insulators  24 A,  24 B,  24 C,  24 D, and  24 E is 135° C., 115° C., 69° C., 28° C., and 117° C., respectively. When the high-temperature and high-humidity test is conducted, it is not preferable if the tensile storage elastic modulus changes significantly around the junction temperature of light emitting elements, and therefore the temperature at which the loss tangent tan δ of the insulator  24  becomes the maximum is preferably 20° C. or higher and lower than 130° C., and, more preferably, 40° C. or higher and lower than 120° C. 
     As can be seen from  FIG. 16  showing the results of the thermal cycle test, with the light emitting devices  10 A,  10 B,  10 C, and  10 D, none of the light emitting devices was turned off even after more than 1000 cycles. However, as can be seen by comparing curve D4, which shows the current-voltage characteristics of the light emitting device  10 D shown in  FIG. 17 , with curves A4, B4 and C4 of the light emitting devices  10 A to  10 C, the light emitting device  10 D suggested a possibility of unstable current-voltage characteristics. 
     As shown in  FIG. 18 , with the light emitting device  10 D, before the thermal cycle test, the current increases regularly, following the increase of the voltage, as shown with curve DO. However, once the thermal cycle test is started, the relationship between the voltage and the current becomes irregular. Consequently, it is possible to say that the light emitting devices  10 A,  10 B, and  10 C have the highest reliability. 
     As shown in  FIG. 15 , in the high-temperature and high-humidity, the light emitting devices  10 A to  10 D, in which the insulators  24  are made of the resins A to D, show good results. Also, as shown in  FIG. 14 , when the humidity is changed from 40% to 85% in which the temperature is 85° C., the expansion coefficients of the resins A to D of the light emitting devices  10 A to  10 D are less than 10%. Therefore, the expansion coefficient of the insulator  24  of the light emitting device  10  is preferably less than 10% when the humidity is changed from 40% to 85% in an environment in which the temperature is 85° C. Furthermore, the expansion coefficient of the insulator  24  is more preferably 4.23% or less. 
     As shown in  FIG. 14 , the water-absorption coefficients of the resins A to D of the light emitting devices  10 A to  10 D are 0.10% or higher in an environment in which the temperature is 85° C. and the humidity is 85%. Therefore, the water-absorption coefficient of the insulator  24  of the light emitting device  10  needs to be 0.10% or higher in an environment in which the temperature is 85° C. and the humidity is 85%. Also, the water-absorption coefficients of the insulator  24  is preferably 0.15% or higher, and, more preferably, 0.3% or higher. 
     Now, although embodiments of the present invention have been described above, the present invention is by no means limited to the embodiments described above. For example, with each of the above-described embodiment, light emitting devices  10  that each have eight light emitting elements  30  have been described. This is by no means limiting, and each light emitting device  10  may have nine or more light emitting elements, or have seven or fewer light emitting elements. Furthermore, light emitting elements  30  of varying standards, such as ones that emit lights of different colors, can be used in a mixed manner. 
     The above-described embodiment have assumed that a light emitting module  20  has a pair of insulators  21  and  22 , an insulator  24  that is formed between the insulators  21  and  22 , and eight light emitting elements  30   1  to  30   8  that are arranged inside the insulator  24 . This is by no means limiting, and, for example, as shown in  FIG. 19 , a light emitting module  20  may be comprised of a plurality of insulators  21  and  22 , a multi-layer circuit that is made of conductor layers  23 , which are formed on the respective surfaces of the insulators  21  and  22  connected by vias  230  formed in via-holes, and light emitting elements  30  that are electrically connected to the multilayer circuit. In this case, by using light emitting elements that have electrodes on the upper surface and the lower surface as light emitting elements  30 , the circuit can be easily multi-layered. 
     Furthermore, light emitting elements to have electrodes on the upper surface and the lower surface can be used for light emitting devices with a single-layer conductor circuit like the light emitting device  10  shown in  FIG. 1 . 
     In this case, a second conductor layer  23  may be formed on the surface of the insulator  22 . 
     Cases have been described with the above embodiments where the conductor layer  23  is made of metal. This is by no means limiting, and the conductor layer  23  may be made of a transparent conductive material such as ITO. 
     Cases have been described with the above embodiments where an insulator  24  is formed, with no gap, between insulators  21  and  22 . This is by no means limiting, and the insulator  24  may be formed between the insulators  21  and  22  only partially. For example, the insulator  24  may be formed only around the light emitting elements. Also, for example, as shown in  FIG. 20 , the insulator  24  may be formed so as to constitute spacers to surround the light emitting elements  30 . 
     Cases have been described with the above embodiments where the light emitting module  20  of a light emitting device  10  has insulators  21  and  22  and an insulator  24 . This is by no means limiting, and, as shown in  FIG. 21 , the light emitting module  20  may be comprised only of an insulator  21  and an insulator  24  that holds light emitting elements  30 . 
     According to the above embodiments, a light emitting device  10  has an insulator  21 , on which a conductor layer  23  is formed, and a light emitting element  30 , with a pair of electrodes  35  and  36  formed on one surface, namely the upper surface. This is by no means limiting, and a light emitting device  10  may have an insulator with conductor layers formed on surfaces that oppose each other, and a light emitting element with electrodes formed on both upper and lower surfaces. 
     The light emitting devices  10  according to the herein-contained embodiments can be used for tail lamps for an automobile. By using a transparent and flexible light emitting module  20  as a light source, a variety of visual effects can be produced.  FIG. 22  is a diagram to show, schematically, a cross-section of a resin casing in a horizontal plane, and its internal structure, with respect to a tail lamp  600  for an automobile. The light emitting device  10  is arranged along the inner surface of the resin casing of the tail lamp  600 , and a mirror M is arranged on the back surface of the light emitting device  10 , so that light that is emitted from the light emitting device  10  toward the mirror M is reflected by the mirror M, and then passes through the light emitting module  20 , and is emitted to the outside. By this means, a unit that is configured as if having a light source apart from the light emitting device  10  in the depth direction of the tail lamp  600  can be formed. 
     The light emitting devices  10  according to the above-described embodiments have assumed that the light emitting elements  30  are arranged on a straight line as shown in  FIG. 4 . This is by no means limiting, and, for example, as shown in  FIG. 23 , the light emitting elements  30  may be arranged in a matrix shape on a two-dimensional plane. 
     The light emitting module  20  of the light emitting device  10  according to the above embodiments, as shown in  FIG. 4 , the light emitting elements  30  are arranged apart from each other. This is by no means limiting, and, for example, as shown in  FIG. 24 , a light emitting element  30 R that glows red, a light emitting element  30 G that glows green, and a light emitting element  30 B that glows blue may be arranged close, so as to form a light emitting element group G, and arranged apart from each other so that the light emitting element group G is recognized as a single bright spot. 
     Although embodiments of the present invention has been described above, the thickness of the insulator  24  according to the embodiments is also disclosed in detail in US Patent Application Publication No. US2016/0155913 (WO2014156159). The bumps  37  and  38  provided in the light emitting element  30  are also disclosed in detail in US Patent Application Publication No. 2016/0276561 (WO/2015/083365). How to connect between the conductor layer  23  and the flexible cable  40  is disclosed in detail in US Patent Application Publication No. US2016/0276321 (WO/2015/083364). The mesh pattern to constitute the conductor layer  23  is disclosed in detail in US Patent Application Publication No. 2016/0276322 (WO/2015/083366). The method of manufacturing the light emitting module  20  is disclosed in detail in US Patent Application Publication No. US2017/0250330 (WO 2016/047134). As shown in  FIG. 23 , a light emitting device in which light emitting elements are arranged in a matrix shape is disclosed in detail in Japanese Patent Application No. 2018-164963. The electrical connection between the bumps  37  and  38  and the conductor layer  23  in the light emitting device is disclosed in detail in Japanese Patent Application No. 2018-16165. Furthermore, the physical properties of the insulator  24  such as mechanical loss tangent are disclosed in detail in Japanese Patent Application No. 2018-164946. The contents disclosed in each of the above applications are incorporated herein by reference. 
     While certain embodiments have been described, these embodiments have been presented by way of example only, and are not intended to limit the scope of the inventions. Indeed, the novel embodiments described herein may be embodied in a variety of other forms; furthermore, various omissions, substitutions and changes in the form of the embodiments described herein may be made without departing from the spirit of the inventions. The accompanying claims and their equivalents are intended to cover such forms or modifications as would fall within the scope and spirit of the inventions.