JP2007258338A - Semiconductor light-emitting element - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a semiconductor light-emitting element capable of increasing light-emitting quantity. <P>SOLUTION: The semiconductor light-emitting element A1 is provided with a supporting substrate 1, a p-GaN layer 2, an n-GaN layer 4 and an active layer 3. A circular n-side electrode 41 is formed on the n-GaN layer 4, and the thickness t of the n-GaN layer 4 satisfies the relation of a formula 1. In the formula, L denotes a representative length of the semiconductor light-emitting element, T denotes the absolute temperature, W denotes the diameter of the n-side electrode, J<SB>0</SB>denotes a current density in a contact portion between the n-side electrode and the n-type semiconductor layer, e denotes an elementary electric charge, γ denotes an ideal coefficient of a diode, κ<SB>B</SB>denotes a Boltzman constant, and ρ denotes a resistivity of the n-type semiconductor layer. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a semiconductor light emitting device having a semiconductor layer.

  As one of the conventional methods for manufacturing a semiconductor light emitting device, after a semiconductor layer is formed on a sapphire substrate, a support substrate is bonded to a portion of the semiconductor layer opposite to the sapphire substrate, and heating by laser light is used. And the method of peeling the said sapphire substrate is used (for example, refer patent document 1). FIG. 10 shows an example of a semiconductor light emitting device manufactured by such a manufacturing method. In the semiconductor light emitting device X shown in the figure, a p-GaN layer 92, an active layer 93, and an n-GaN layer 94 as semiconductor layers are stacked on a support substrate 91 on which a p-side electrode 91a is formed. It is structured. An n-side electrode 94 a is formed on the upper surface of the n-GaN layer 94. The holes from the p-GaN layer 92 and the electrons from the n-GaN layer 94 are recombined in the active layer 93, whereby the semiconductor light emitting device X emits light.

  However, electrons injected from the n-side electrode 94 a are likely to penetrate the n-GaN layer 94 due to a potential difference in the thickness direction of the n-GaN layer 94. For this reason, sufficient current does not flow near the end of the n-GaN layer 94. Then, it becomes difficult to recombine electrons and holes in the entire active layer 93. Therefore, it is difficult for the semiconductor light emitting device X to emit light efficiently with respect to input power.

JP-A-2003-168820

  The present invention has been conceived under the circumstances described above, and an object thereof is to provide a semiconductor light emitting element capable of increasing the amount of light emission.

ここで、
Ｌ：上記半導体発光素子の代表長さ
Ｔ：絶対温度
Ｗ：上記ｎ側電極の直径
Ｊ₀：上記ｎ側電極と上記ｎ型半導体層との接触部分における電流密度
ｅ：素電荷
γ：ダイオードの理想係数
κ_B：ボルツマン定数
ρ：上記ｎ型半導体層の比抵抗 A semiconductor light-emitting device provided by the first aspect of the present invention is disposed on a substrate, a p-type semiconductor layer supported by the substrate, and a position separated from the p-type semiconductor layer with respect to the substrate. A semiconductor light emitting device comprising: an n-type semiconductor layer; and an active layer disposed between the p-type semiconductor layer and the n-type semiconductor layer, wherein the n-type semiconductor layer includes a circular n-side. An electrode is formed, and the n-type semiconductor layer is characterized in that the thickness t satisfies the relationship of Formula 1.

here,
L: representative length of the semiconductor light emitting element T: absolute temperature W: diameter of the n-side electrode J ₀ : current density at the contact portion between the n-side electrode and the n-type semiconductor layer e: elementary charge γ: diode Ideal coefficient κ _B : Boltzmann constant ρ: Specific resistance of the n-type semiconductor layer

  The representative length of the semiconductor light-emitting element referred to in the present invention refers to, for example, a diameter in a circular shape and a length of one side in a rectangular shape.

  According to such a configuration, a current can flow through a wide region of the n-type semiconductor layer. Thereby, electrons and holes can be recombined in the entire area of the active layer. Therefore, the light emission amount of the semiconductor light emitting element can be increased.

ただし、０．１μｍ≦ｘ≦３．０μｍ In a preferred embodiment of the present invention, a plurality of convex portions are formed in the n-type semiconductor layer, and the thickness t of the n-type semiconductor layer satisfies the relationship of Equation 2.

However, 0.1 μm ≦ x ≦ 3.0 μm

  According to such a configuration, it is possible to prevent light from the active layer from being totally reflected on the surface of the n-type semiconductor layer. Therefore, the emission efficiency from the n-type semiconductor layer can be increased, and the light emission amount of the semiconductor light emitting element can be further increased.

  In a preferred embodiment of the present invention, the n-type semiconductor layer is made of n-GaN. According to such a configuration, the semiconductor light emitting element can be configured to emit blue light or green light.

ここで、
Ｌ：上記半導体発光素子の代表長さ
Ｔ：絶対温度
Ｗ：上記ｎ側電極の直径
Ｊ₀：上記ｎ側電極と上記ｎ型半導体層との接触部分における電流密度
ｅ：素電荷
γ：ダイオードの理想係数
κ_B：ボルツマン定数
ρ：上記ｎ型半導体層の比抵抗 A semiconductor light-emitting device provided by the second aspect of the present invention is disposed on a substrate, a p-type semiconductor layer supported by the substrate, and a position spaced apart from the p-type semiconductor layer with respect to the substrate. A semiconductor light emitting device comprising: an n-type semiconductor layer; and an active layer disposed between the p-type semiconductor layer and the n-type semiconductor layer, wherein the n-type semiconductor layer has a rectangular shape, An n-side electrode having the same width as that of the n-type semiconductor layer is formed, and the n-type semiconductor layer has a thickness t satisfying the relationship of Equation 3.

here,
L: representative length of the semiconductor light emitting element T: absolute temperature W: diameter of the n-side electrode J ₀ : current density at the contact portion between the n-side electrode and the n-type semiconductor layer e: elementary charge γ: diode Ideal coefficient κ _B : Boltzmann constant ρ: Specific resistance of the n-type semiconductor layer

  According to such a configuration, even if the n-side electrode has a rectangular shape having the same width as the n-type semiconductor layer, it is the same as the semiconductor light emitting device provided by the first aspect of the present invention. In addition, a current can flow through a wide region of the n-type semiconductor layer. Therefore, the light emission amount of the semiconductor light emitting element can be increased.

ただし、０．１μｍ≦ｘ≦３．０μｍ In a preferred embodiment of the present invention, the n-type semiconductor layer has a plurality of convex portions, and the thickness of the n-type semiconductor layer satisfies the relationship of Equation 4.

However, 0.1 μm ≦ x ≦ 3.0 μm

  According to such a configuration, the emission efficiency from the n-type semiconductor layer can be increased, and the light emission amount of the semiconductor light emitting element can be further increased.

  In a preferred embodiment of the present invention, the n-type semiconductor layer is made of n-GaN. According to such a configuration, the semiconductor light emitting element can be configured to emit blue light or green light.

  Other features and advantages of the present invention will become more apparent from the detailed description given below with reference to the accompanying drawings.

  Hereinafter, preferred embodiments of the present invention will be specifically described with reference to the drawings.

  FIG. 1 shows a first embodiment of a semiconductor light emitting device according to the present invention. The semiconductor light emitting device A1 of the present embodiment includes a support substrate 1, a p-side electrode 21, a reflective layer 22, a mask layer 23, a ZnO electrode 24, a p-GaN layer 2, an active layer 3, an n-GaN layer 4, and an n side. An electrode 41 is provided, and is configured to emit blue light or green light, for example. In the present embodiment, the n-side electrode 41 has a circular shape.

  The support substrate 1 supports the p-side electrode 21, the reflective layer 22, the mask layer 23, the ZnO electrode 24, the p-GaN layer 2, the active layer 3, the n-GaN layer 4, and the n-side electrode 41. The support substrate 1 is made of a material having high thermal conductivity such as Cu or AlN. Thereby, the support substrate 1 exhibits the function to dissipate the heat generated when the semiconductor light emitting element A1 is energized to the outside.

  The p-side electrode 21 is formed over the entire upper surface of the support substrate 1 in the figure. The p-side electrode 21 is made of, for example, Au—Sn or Au.

  The reflective layer 22 has a structure in which, for example, Al, Ti, Pt, and Au are stacked in order from the top in the figure. By having a layer made of Al having a relatively high reflectance, the reflection layer 22 can reflect light emitted from the active layer 3 upward in the figure. Further, the reflective layer 22 makes the p-side electrode 21 and the ZnO electrode 24 conductive. Ag may be used instead of Al.

The mask layer 23 is used as an etching mask when the ZnO electrode 24, the p-GaN layer 2, the active layer 3, and the n-GaN layer 4 are etched in the manufacturing process of the semiconductor light emitting element A <b> 1 described later. The mask layer 23 is made of a dielectric material such as SiO ₂ . In the mask layer 23, a plurality of through holes 23a are formed. The plurality of through-holes 23a are for bringing the reflective layer 22 and the ZnO electrode 24 into contact with each other by bringing them into contact with each other. In the present embodiment, the plurality of through holes 23 a are arranged concentrically around a point located directly below the n-side electrode 41.

The ZnO electrode 24 is made of ZnO, which is one of transparent conductive oxides, and allows the n-GaN layer 4 and the reflection layer 22 to conduct while transmitting light from the active layer 3. The ZnO electrode 24 has a relatively low resistivity of about 2 × 10 ⁻⁴ Ωcm and a thickness of about 1000 to 20000 mm.

  The p-Gan layer 2 is a layer made of GaN doped with Mg, which is a p-type dopant, and is an example of a p-type semiconductor layer referred to in the present invention. An undoped GaN layer (not shown) or an InGaN layer (not shown) containing about 1% In is formed between the p-GaN layer 2 and the active layer 3.

The active layer 3 is a layer having an MQW structure containing InGaN, and is a layer for amplifying light emitted by recombination of electrons and holes. The active layer 3 has a structure in which a plurality of InGaN layers are stacked. These InGaN layers have a composition of In _X Ga _{1 -X} N (0 ≦ X ≦ 0.3) and In _Y Ga _{1 -Y} N (0 ≦ Y ≦ 0.1 and Y ≦ X). There are two types. A layer made of In _X Ga ₁ -XN is a well layer, and a layer made of In _Y Ga ₁ -YN is a barrier layer. These well layers and barrier layers are alternately stacked. A superlattice layer (not shown) made of Si-doped InGaN and GaN is formed between the active layer 3 and the n-GaN layer 4.

  The n-GaN layer 4 is a layer made of GaN doped with Si, which is an n-type dopant, and is an example of an n-type semiconductor layer referred to in the present invention. An n-side electrode 41 is formed on the n-GaN layer 4. The n-side electrode 41 has a structure in which, for example, Al, Ti, Au or Al, Mo, Au are stacked in order from the n-GaN layer 4 side.

  Here, a method of determining the thickness t of the n-GaN layer 4 will be described below with reference to FIG. FIG. 2 shows an enlarged view of part of the n-GaN layer 4 and the n-side electrode 41. In this figure, the n-GaN layer 4 and the n-side electrode 41 are substantially circular. First, the resistance dR when the current flows from r → r + dr is given by Equation 5.

ここで、ρはｎ−ＧａＮ層４の比抵抗である。

Here, ρ is the specific resistance of the n-GaN layer 4.

  Assuming that the diameter of the n-GaN layer 4 at which the current density is 1 / e due to current traveling from the end of the n-side electrode 41 to the end of the n-GaN layer 4, the n-side electrode at this time The resistance R from the end of 41 to the end of the n-GaN layer 4 is obtained by Equation 6.

ここで、Ｗはｎ側電極４１の直径である。

Here, W is the diameter of the n-side electrode 41.

On the other hand, when the current density immediately below the n-side electrode 41 is J ₀ , the current I flowing from the n-type electrode 41 through the n-GaN layer 4 is expressed by Equation 7.

  Further, according to the forward current voltage characteristics of the pn junction semiconductor, the current I is expressed by Equation 8.

ここで、Ｖは電圧、γは半導体発光素子の理想係数、κ_Bはボルツマン定数、Ｔは絶対温度である。たとえば、ＧａＮの理想係数γは、一般的に２〜３程度であるが、ＧａＮの結晶成長状態などによって個別に変化する値である。

Here, V is a voltage, γ is an ideal coefficient of the semiconductor light emitting element, κ _B is a Boltzmann constant, and T is an absolute temperature. For example, the ideal coefficient γ of GaN is generally about 2 to 3, but is a value that varies individually depending on the crystal growth state of GaN.

  From Expression 8, the voltage V at which the current I becomes 1 / e is Expression 9.

  Substituting Equations 6, 7, and 9 into Ohm's equation IR = V yields Equation 10. As a result, the thickness t required to set the current to 1 / e is expressed as Equation 11.

  From the above, in order to sufficiently spread the current in the in-plane direction in the n-GaN layer 4, the thickness t should satisfy the relationship of Equation 12.

In the present invention, the representative length of the n-type semiconductor layer refers to the diameter when they are circular, and refers to the length of one side when they are rectangular. In the present embodiment, when the diameter W of the n-side electrode 41 is about 100 μm and the diameter of the n-GaN layer 4 or the length L of one side is about 250 μm, the specific resistance ρ is 7.8 × 10 ⁻⁵ Ωcm. , the current density J ₀ is ^{2.5 × 10 6 a / m 2} , the ideality factor γ is 2, the Boltzmann factor kappa _B is a 1.38 × 10- ²³ J / Kmol, the thickness of the n-GaN layer 4 t May be 1.1 μm or more.

  Next, a method for manufacturing the semiconductor light emitting element A1 will be described below with reference to FIGS.

First, the sapphire substrate 50 is placed in a growth chamber for MOCVD. While supplying H ₂ gas into the growth chamber, the temperature in the growth chamber is set to about 1,050 ° C., thereby cleaning the sapphire substrate 50.

Next, using MOCVD, a GaN buffer layer (not shown) is formed on the sapphire substrate 50 in a state where the film formation temperature, which is the temperature in the growth chamber, is set to about 600 ° C., and then the film formation temperature is set. An n-GaN layer 4 with Si as a dopant at a temperature of about 1000 ° C., an InGaN-GaN superlattice layer (not shown) with Si as a dopant, an MQW active layer 3, and an undoped GaN layer or about 1% InGaN layers (not shown) containing In are sequentially stacked. Next, the p-GaN layer 2 using Mg as a dopant is formed with the growth temperature slightly raised. The p-GaN layer 2 is annealed to activate Mg. Then, the ZnO electrode 24 is formed using MBE (Molecular Beam Epitaxy) method. Thereafter, a mask layer 23 made of SiO ₂ is formed.

  Next, as shown in FIG. 4, a resist film 51 is formed by a photolithography technique. Thereafter, the mask layer 23 is patterned by etching using the resist film 51 as a mask. Then, the resist film 51 is removed. Mesa etching from the ZnO electrode 24 to the n-GaN layer 4 is performed by ICO (inductively coupled plasma) etching using the mask layer 23.

Next, as shown in FIG. 5, the mask layer 23 is patterned by dry etching using CF ₄ gas. Thereby, a plurality of through holes 23 a arranged concentrically for contacting the reflective layer 22 and the ZnO electrode 24 are formed in the mask layer 23. At this time, the ZnO electrode 24 functions as an etching stopper. After forming the plurality of through holes 23a, a resist film 52 is formed. Also, Al or Ag is vapor-deposited, and Ti, Pt, and Au are sequentially laminated to form the metal layer 22A. Then, the reflective layer 22 is formed by removing the resist film 52 and a part of the metal layer 22A.

  Next, as shown in FIG. 6, a support substrate 1 is prepared, and a p-side electrode 21 made of Au—Sn or Au is formed on the support substrate 1. The p-side electrode 21 and the reflective layer 22 are joined by thermocompression bonding. Thereafter, a KrF laser oscillating at about 248 nm is irradiated through the sapphire substrate 50 toward the n-GaN layer 4. Thereby, the interface between the sapphire substrate 50 and the n-GaN layer 4 (the GaN buffer layer (not shown) described above) is rapidly heated. Then, the n-GaN layer 4 near the interface and the GaN buffer layer are dissolved, and the sapphire substrate 50 can be peeled off. This process is generally called an LLO (Laser Lift Off) process.

  Next, a metal layer (not shown) made of Al, Ti, Au or Al, Mo, Au is formed on the n-GaN layer 4. By patterning this metal layer, the n-side electrode 41 shown in FIG. 1 is formed. Through the above steps, the semiconductor light emitting element A1 is obtained.

  Next, the operation of the semiconductor light emitting element A1 will be described.

  According to the present embodiment, since the thickness t of the n-GaN layer 4 satisfies the relationship of Equation 12, the current from the n-side electrode 41 causes the n-GaN layer 4 to move in the thickness direction. This current can be sufficiently spread in the in-plane direction of the n-GaN layer 4 before passing. As a result, current can flow through each of the n-GaN layer 4, the active layer 3, and the p-GaN layer 2. Therefore, it is possible to emit light reasonably by using the entire active layer 3, and the light amount of the semiconductor light emitting element A1 can be increased.

  Further, the current flowing through the semiconductor light emitting element A1 flows through the n-side electrode 41 and the plurality of through holes 23a. Since the plurality of through holes 23a are arranged concentrically with respect to the center located immediately below the n-side electrode 41, the current flowing through the semiconductor light emitting element A1 is easily spread in the width direction of the semiconductor light emitting element A1. ing. With such a configuration, light emission from the entire active layer 3 can be further promoted.

  7 and 8 show a second embodiment of a semiconductor light emitting device according to the present invention and a method for manufacturing the same. In these drawings, the same or similar elements as those in the above embodiment are denoted by the same reference numerals as those in the above embodiment.

  In the semiconductor light emitting device A2 shown in FIG. 7, a plurality of convex portions 4a are formed on the upper surface of the n-GaN layer 4 in the drawing. The convex portion 4a has a cone shape. In the present embodiment, the width Wc of the bottom of the convex portion 4a is the average value Wc of the width Wc when the peak wavelength of light emitted from the active layer 3 is λ and the refractive index of the n-GaN layer 4 is n. 'Satisfies the relationship of Wc' = λ / n. For example, when the peak wavelength λ of light from the active layer 3 is 460 nm and the refractive index n of the n-GaN layer 4 is about 2.5, Wc ′ is about 184 nm or more. Moreover, in this embodiment, the height of the convex part 4a is about 2 micrometers.

  In the semiconductor light emitting device A2, the thickness t of the n-GaN layer 4 satisfies the relationship of the following mathematical formula 13.

ただし、０．１μｍ≦ｘ≦３．０μｍ

However, 0.1 μm ≦ x ≦ 3.0 μm

  Formula 13 is obtained by adding a (+ x) term to the right side of Formula 12. This increase in x corresponds to the height of the convex portion 4a described above.

In order to manufacture the semiconductor light emitting device A2, the n-side electrode 41 is formed as shown in FIG. 8 from the state of FIG. 6 described above. In FIG. 6, the surface of the n-GaN layer 4 after the sapphire substrate 50 is peeled is not a Ga polar face but an N polar face where anisotropy is likely to occur by etching. In this state, as shown in FIG. 8, while immersing the n-GaN layer 4 in about 4 mol / l KOH solution at about 62 ° C., irradiation with ultraviolet (UV) light of about 3.5 W / cm ² is performed for about 10 minutes. To do. Thereby, a plurality of convex portions 4a satisfying the above-described relationship can be formed on the surface of the n-GaN layer 4 with the average value Wc ′ of the width Wc of the bottom surface. As a result, the thickness t of the n-GaN layer 4 can satisfy the relationship of Equation 13.

  Even in such an embodiment, the amount of light emitted from the active layer 3 can be increased. Further, by forming a plurality of convex portions 4 a on the surface of the n-GaN layer 4, the light from the active layer 3 is totally reflected on the surface of the n-GaN layer 4 and returns to the inside of the n-GaN layer 4. Can be suppressed. Therefore, it is suitable for increasing the light amount of the semiconductor light emitting element A2.

  Next, the case where the shape and size of the n-side electrode 41 are different from those of the above-described embodiment will be described below. In the present embodiment, the cross-sectional shape is as shown in FIG. 1, the n-side electrode 41 is rectangular, and the width thereof is the same as the width of the n-GaN layer 4. FIG. 9 is an enlarged perspective view of the n-side electrode 41 and the n-GaN layer 4 in the present embodiment. Below, the determination method of the thickness t of the n-GaN layer 4 in this embodiment is demonstrated.

  First, the current advances from the end of the n-side electrode 41 to the end of the n-GaN layer 4, so that the length of the n-GaN layer 4 at which the current density becomes 1 / e is set to L, the n-GaN layer. When the width is y, the resistance R from the end of the n-side electrode 41 to the end of the n-GaN layer 4 at this time can be obtained by Expression 14.

On the other hand, when the current density immediately below the n-side electrode 41 is J ₀ , the current I flowing from the n-type electrode 41 through the n-GaN layer 4 is expressed by Equation 15.

  Further, according to the forward current-voltage characteristics of the pn junction semiconductor, the current I is expressed by the above-described formula 8. Further, the voltage V at which the current I becomes 1 / e is given by the above-described formula 9. Substituting Equations 14, 15, and 9 into Ohm's equation IR = V yields Equation 16. As a result, the thickness t required to set the current to 1 / e is expressed as Equation 17.

  From the above, in order to sufficiently spread the current in the in-plane direction in the n-GaN layer 4, the thickness t should satisfy the relationship of Equation 18.

  Further, in the configuration in which the n-side electrode 41 is rectangular and has the same width as the n-GaN layer 4, a plurality of convex portions 4a are formed on the upper surface of the n-GaN layer 4 as in the configuration shown in FIG. A configuration may be adopted. In this case, the thickness t of the n-GaN layer 4 is determined by Equation 19.

ただし、０．１μｍ≦ｘ≦３．０μｍ

However, 0.1 μm ≦ x ≦ 3.0 μm

  Also according to these embodiments, the current flowing through the n-GaN layer 4 can be spread to the peripheral portion of the n-GaN layer 4, and the amount of light emission can be increased. Further, when the plurality of convex portions 4a are formed, it is possible to expect a further increase in light emission amount as described above.

  The semiconductor light emitting device according to the present invention is not limited to the above-described embodiment. The specific configuration of each part of the semiconductor light emitting device according to the present invention can be varied in design in various ways.

  The n-type semiconductor layer and the p-type semiconductor layer referred to in the present invention are not limited to the n-GaN layer and the p-GaN layer, and may be any semiconductor layer that can inject electrons and holes into the active layer. The thickness of the n-type semiconductor layer may be represented by the formulas 1 to 4 using the physical property values of the semiconductor material. The active layer referred to in the present invention is not limited to the MQW structure. The semiconductor light emitting device according to the present invention can be configured to emit light of various wavelengths such as white light in addition to blue and green light.

It is sectional drawing which shows 1st Embodiment of the semiconductor light-emitting device based on this invention. It is a principal part expansion perspective view of the semiconductor light-emitting device shown in FIG. FIG. 2 is a cross-sectional view showing a step of stacking a semiconductor layer on a sapphire substrate in the manufacturing process of the semiconductor light emitting device shown in FIG. FIG. 4 is a cross-sectional view showing a semiconductor layer etching step in the manufacturing process of the semiconductor light emitting device shown in FIG. 1. FIG. 3 is a cross-sectional view showing a step of forming a reflective layer in the manufacturing process of the semiconductor light emitting device shown in FIG. 1. It is sectional drawing which shows the process of peeling a sapphire substrate in the manufacturing process of the semiconductor light-emitting device shown in FIG. It is sectional drawing which shows 2nd Embodiment of the semiconductor light-emitting device based on this invention. FIG. 8 is a cross-sectional view showing a step of forming a plurality of convex portions in the manufacturing process of the semiconductor light emitting device shown in FIG. 7. It is a principal part expansion perspective view of the other example of the semiconductor light-emitting device based on this invention. It is sectional drawing which shows an example of the conventional semiconductor light-emitting device.

Explanation of symbols

A1, A2 Semiconductor light emitting element 1 Support substrate (substrate)
2 p-GaN layer (p-type semiconductor layer)
3 Active layer 4 n-GaN layer (n-type semiconductor layer)
21 p-side electrode 41 n-side electrode 22 reflective layer 23 mask layer 24 ZnO electrode 50 sapphire substrate

Claims (6)

A substrate,
A p-type semiconductor layer supported by the substrate;
An n-type semiconductor layer disposed at a position away from the p-type semiconductor layer with respect to the substrate;
A semiconductor light emitting device comprising an active layer disposed between the p-type semiconductor layer and the n-type semiconductor layer,
In the n-type semiconductor layer, a circular n-side electrode is formed,
The n-type semiconductor layer has a thickness t satisfying the relationship of Formula 1;

here,
L: representative length of the semiconductor light emitting element T: absolute temperature W: diameter of the n-side electrode J ₀ : current density at the contact portion between the n-side electrode and the n-type semiconductor layer e: elementary charge γ: diode Ideal coefficient κ _B : Boltzmann constant ρ: Specific resistance of the n-type semiconductor layer The n-type semiconductor layer has a plurality of convex portions,
The semiconductor light-emitting element according to claim 1, wherein the n-type semiconductor layer has a thickness t satisfying the relationship of Formula 2.

However, 0.1 μm ≦ x ≦ 3.0 μm   The semiconductor light-emitting element according to claim 1, wherein the n-type semiconductor layer is made of n-GaN. A substrate,
A p-type semiconductor layer supported by the substrate;
An n-type semiconductor layer disposed at a position away from the p-type semiconductor layer with respect to the substrate;
A semiconductor light emitting device comprising an active layer disposed between the p-type semiconductor layer and the n-type semiconductor layer,
The n-type semiconductor layer is formed with an n-side electrode having a rectangular shape and the same width as the width of the n-type semiconductor layer,
The n-type semiconductor layer has a thickness t that satisfies the relationship of Equation 3.

here,
L: representative length of the semiconductor light emitting element T: absolute temperature W: diameter of the n-side electrode J ₀ : current density at the contact portion between the n-side electrode and the n-type semiconductor layer e: elementary charge γ: diode Ideal coefficient κ _B : Boltzmann constant ρ: Specific resistance of the n-type semiconductor layer The n-type semiconductor layer has a plurality of convex portions,
The semiconductor light-emitting element according to claim 4, wherein the n-type semiconductor layer has a thickness t satisfying the relationship of Expression 4.

However, 0.1 μm ≦ x ≦ 3.0 μm   The semiconductor light emitting element according to claim 4, wherein the n-type semiconductor layer is made of n-GaN.

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