TW201633559A - Light-emitting element and method for manufacturing same - Google Patents

Abstract

A semiconductor light-emitting element with a reflective film disposed on a front surface (side) of a GaN substrate and with a photonic crystal periodic structure disposed on a rear surface (side) of the GaN substrate, the photonic crystal periodic structure being such that the design wavelength [lambda]V in vacuum, a period a as a periodic structure parameter, and a radius R satisfy the Bragg condition, wherein, in a range of R/a of 0.18 to 0.40, a TM light photonic band structure has two photonic bandgaps within the fourth photonic band.

Description

Light-emitting element and method of manufacturing same

The present invention relates to a light-emitting element and a method of manufacturing the same.

According to the semiconductor light-emitting element represented by a light-emitting diode (LED) or an organic EL (OLED), as a light source for display and illumination purposes, in order to achieve high brightness, it is generally used to form a micron-sized unevenness on the surface. A sapphire substrate (PSS: patterned sapphire substrate) to improve light extraction efficiency. The performance of the LED is expressed by external quantum efficiency (EQE), which is the product of internal quantum efficiency (IQE), electron injection efficiency (EIE), and light extraction efficiency (LEE) (IQE × EIE × LEE). Since the GaN substrate LED has no lattice strain and does not cause crystal defects at the interface, and has excellent heat dissipation properties as a conductive substrate, the value of IQE × EIE is extremely excellent. However, the refractive index of GaN is 2.5 at a wavelength of 455 nm, and the emitted light is totally reflected by 80% or more at the interface between GaN and air, and disappears internally, so that the light extraction efficiency is poor. As a new method for improving the efficiency of light extraction, a technique for forming a periodic structure of a photonic crystal having a period of a wavelength of light in a light extraction layer has been described. The periodic structure of the photonic crystal is formed at the interface of two structures having different refractive indices, and is generally mainly a concavity and convexity having a column structure or a pore structure. Further, it is known that the total light emission is suppressed in the region where the periodic structure is formed, thereby suppressing total reflection, and the use of this point contributes to an improvement in light extraction efficiency (see Patent Document 1).

In the light-emitting element described in the following Patent Document 2, the main light extraction surface is formed into a flip-chip structure of an n-type semiconductor layer, and a concave portion having two or more inclined surfaces is formed on the back surface thereof to improve light extraction efficiency. Furthermore, the light is efficiently emitted above the concave portion The way to control the light distribution.

[Previous Technical Literature]

[Patent Literature]

[Patent Document 1] Japanese Patent No. 5315513

[Patent Document 2] Japanese Patent Laid-Open Publication No. 2010-74008

The photonic crystal system produced in the light-emitting element described in Patent Document 1 has an object for improving light extraction efficiency, but does not disclose control of light distribution.

In the concave portion having two or more inclined surfaces produced in the light-emitting element described in Patent Document 2, since it is necessary to precisely control the angle of each inclined surface and the size of the bottom surface of the concave portion, there is a problem that the manufacturing steps become complicated.

An object of the present invention is to provide a light-emitting element having high light extraction efficiency from the back surface of a GaN substrate and excellent light distribution property, and a method of manufacturing the same.

According to the present invention, there is provided a light-emitting element having a reflective film on a surface (side) of a GaN substrate, a photonic crystal periodic structure including two structures having different refractive indices on a back surface (side) of the GaN substrate, and the photons described above The periodic structure of the crystal has a photonic crystal on the back side of the GaN substrate, and the design wavelength λ _V and the periodic structure parameters in the vacuum, that is, the period a and the radius R satisfy the Bragg condition, and the ratio R/a varies from 0.18 to 0.40. when the photon energy of light with TM (PB) structure of the photonic band in the fourth (4 _th PB) is present within two photonic bandgap (PBG), corresponding to the maximum value of each photonic band gap R / a is a number m=3~4.

Or, providing a light-emitting element having a photonic crystal on the back surface of the GaN substrate, that is, when the vertical axis (ωa/2πc) of the photonic band structure is converted into a wavelength λ _V in a vacuum, in the second photon energy band ( The symmetry point of 2 _nd PB), that is, the point of the Γ point, the M point, and the K point, is the number of times R=a when the point is the closest or the closest to the wavelength λ _V ×m in the vacuum m=3~4 A photonic crystal formed. Or, providing a light-emitting element having a photonic crystal on the back surface of the GaN substrate, that is, when the number of times m=3, the wavelength λ _V × 3 in the vacuum from the vertical axis and the fourth photon energy band (4 _th PB) R is set to an integral multiple of 4 and 5 each an integral multiple of a fourth photon energy band (4 _th PB) of any point on a symmetrical point of contact or closest to the / a configuration of a photonic crystal.

Or, a light-emitting element having a photonic crystal on the back surface of the GaN substrate is provided, that is, when the number of times m=4, the wavelength λ _V × 4 in the vacuum from the vertical axis and the fourth photon energy band (4 _th PB) R 5 is set to an integer multiple of an integer multiple of 6, each fourth photonic band 7 integral multiple of a point of symmetry on either of (4 _th PB) or closest to the contact point / a configuration of a photonic crystal.

Further, there is provided a light-emitting element having a photonic crystal on the back surface of a GaN substrate, that is, a photonic crystal composed of each of R/a selected in the foregoing and a depth h of 0.5 a or more is simulated by an FDTD method to extract light Photonic crystals that are ultimately determined by efficiency and light distribution.

Furthermore, the present invention is a method for calculating a parameter of a periodic structure of a photonic crystal, which is characterized in that it is used in the above-described semiconductor light-emitting device, and the method has a first step, which is a parameter of a tentative periodic structure, that is, a period a ratio of a to the radius R of the structure (R/a); and a second step of calculating the average refractive index n ₁ and n ₂ from the structure, and calculating the average from the refractive indices and the R/a The refractive index n _av is substituted into the Bragg conditional expression, and the period a and the radius R are obtained for the number of times m=3 and m=4; the third step is performed by using the aforementioned R/a and the aforementioned wavelength λ and The planar wave expansion method of the dielectric coefficients ε1 and ε2 of the respective structures obtained by the refractive indices n1 and n2, and the photon energy band structure of the TM light is analyzed; and the fourth step is to use the second photon energy band of the TM light (2) a longitudinal axis (ωa / 2πc) _nd PB) and a fourth photonic band (4 _th PB) in terms of the vacuum wavelength λ _V, to obtain a number of m = 1 and _V [lambda] photon ka / 2π by the band structure; In the fifth and sixth steps, the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) of the TM light are obtained for the number of times m=3 and m=4. The wavelength λ _V × m in the vacuum in each of the symmetry points is the point of convergence or the closest R/a, and is set as the best candidate; and the seventh step is for 0.18 ≦R/a ≦ 0.40 All the R/a times m=3 and 4 use the finite time domain difference method (FDTD method) to calculate the light extraction efficiency increase and decrease rate and light distribution of the photonic crystal corresponding to the above R/a, and the number of times of the depth system m=3~4 select any value of 0.5 times or more of the maximum period a.

Alternatively, the present invention provides a parameter calculation method for a periodic structure of a photonic crystal, which is characterized in that it is used in the above-described semiconductor light-emitting element, and the method has the first step, which is a parameter of a tentative periodic structure, that is, a period a ratio of a to the radius R of the structure (R/a); and a second step of calculating the average refractive index from the respective refractive indices n1 and n2 of the structure and from the above-mentioned R/a n _av , and substituting it into the Bragg conditional expression, obtaining the period a and the radius R for the number of times m=3 and m=4; the third step, which is performed by using the aforementioned R/a and the aforementioned wavelength λ and the aforementioned refraction The plane wave expansion method of the dielectric coefficients ε1 and ε2 of the respective structures obtained at n1 and n2, and the photon energy band structure of the TM light is analyzed; the fourth step is to use the second photon band of the TM light (2 _nd PB) a longitudinal axis (ωa / 2πc)) photonic band and the fourth (4 _th PB) in terms of the vacuum wavelength λ _V, to obtain a number of m = 1 and _V [lambda] photon ka / 2π by the band structure; 5 And the sixth step, which is to determine the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) with TM light for the number of times m=3 and m=4. The wavelength λ _V × m in the vacuum in each symmetry point is connected by point or the closest R/a, and is set as the best candidate; the seventh step is for 0.18 ≦R/a ≦ 0.40 All the R/a times m=3 and 4 use the finite time domain difference method (FDTD method) to calculate the light extraction efficiency increase and decrease rate and light distribution of the photonic crystal corresponding to the above R/a, and the depth system is m =3~4 selects any value of 0.5 times or more of the maximum period a; and the eighth step, which is selected from the target R/a and the number m of the light extraction efficiency (LEE) increase and decrease ratio The R/a and the number of times m of the light distribution determine the diameter, the period, and the depth, and the R/a which is the best candidate for the photonic crystal obtained in the third step to the sixth step, and other R/ When a is compared, the parameter with good light distribution is selected.

Next, the present invention provides a light-emitting element having a photonic crystal on the back surface of a GaN substrate, wherein the photonic crystal system utilizes a nano-molding method in which a pattern is collectively transferred on an organic resist spin-coated on a substrate. Production.

In particular, the present invention provides a light-emitting element having a photonic crystal on the back side of a GaN substrate, the photonic crystal being formed by a two-layer resist process having: a spin-on-substrate etching option on a substrate a step of comparing a large underlayer resist; a step of spin coating a resist having a fluidity and an oxygen resistance function on the underlying resist and transferring a photonic crystal pattern on the upper layer; a step of applying a layer of resist to the oxygen plasma to impart oxygen resistance; and patterning the upper layer resist having the aforementioned oxygen resistance as a mask to form a pattern on the underlying resist using oxygen plasma And the step of dry etching the substrate by ICP plasma using the patterned underlying resist as a mask.

The present disclosure contains the disclosure of Japanese Patent Application No. 2014-248769, which is the priority of the present disclosure.

According to the present invention, there is provided a light-emitting element which has high light extraction efficiency from the back surface of a GaN substrate and is excellent in light distribution.

1‧‧‧Al reflective film/Al reflective electrode

3‧‧‧ITO transparent electrode

5‧‧‧p-type GaN layer

7‧‧‧GaN active layer (light-emitting layer) / p-type GaN light-emitting layer

11‧‧‧n-type GaN layer

15‧‧‧GaN substrate

15a‧‧‧Back/Interface

17‧‧‧Photonic crystal structure (phc)/photonic crystal structure/photonic crystal periodic structure

17a‧‧‧GaN column structure/column structure rod (column)

17b‧‧‧air

A‧‧ cycle

B1‧‧‧ distance

B1+b2‧‧‧distance

-b1‧‧‧distance

-b1-b2‧‧‧Distance

B2‧‧‧ distance

-b2‧‧‧distance

B1+b2‧‧‧distance

d ₁ ‧‧‧diameter

d ₂ ‧‧‧diameter

G‧‧‧thickness

H‧‧‧depth

K‧‧ symmetry point

PBG‧‧‧ photonic band gap

PBG1‧‧‧ photonic band gap

PBG2‧‧‧ photonic band gap

PBG3‧‧‧ photonic band gap

R‧‧‧ Radius

R/a‧‧ ratio

S1‧‧‧ steps

S2‧‧‧ steps

S3‧‧‧ steps

S4‧‧‧ steps

S5‧‧ steps

S6‧‧ steps

S7‧‧ steps

S8‧‧‧ steps

M‧‧‧ times

M‧‧ symmetry point

Γ‧‧ symmetry point

Θ‧‧‧ angle

Φ‧‧‧ angle

Fig. 1 is a cross-sectional structural view (Fig. 1 (a)) and a plan view (Fig. 1 (b)) showing a configuration example of a light-emitting device according to an embodiment of the present invention.

Fig. 2 is a view showing the state of transmission of light of TM light for the purpose of transmission for the optimization of the parameters of the periodic structure.

Fig. 3 is a view showing a first Brillouin region, and further showing a map of Γ, M, and K points (symmetric points).

Figure 4 is a diagram showing the structure of a lattice-free band in a uniform medium required in a region surrounded by symmetrical dots.

Figure 5 is a diagram showing the photonic band (PB) structure of photonic crystal TM light.

6 shows the photonic band gap (PBG) between 1 _st PB-2 _nd PB, 3 _rd PB-4 _th PB, and 5 _th PB-6 _th PB as PBG1, PBG2, and PBG3, respectively, and R/ is displayed. A diagram of the relationship between a and PBG.

Fig. 7A shows that the vertical axis (ωa/2πc) of the second photon energy band (2 _nd PB) satisfying the Bragg condition is converted into the wavelength λ _V in the vacuum, and the photon of λ _V and ka/2π when the number m = 1 A diagram with a structure.

7B, the fourth line displays satisfy the Bragg conditions of photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V, to the number of photons when m = 1 and λ _V ka / 2π of A diagram with a structure.

Fig. 8A is a diagram showing R/a determined by the number of times m = 3, and a second photon energy band (2 _nd PB) of R/a = 0.37 (number of times m = 1) in step 4 generates a standing wave.

FIG. 8B lines showed a number of times m = 3 R determined by the / a of the FIG, and a display-based R / a photonic band of a fourth (4 _th PB) to produce a standing wave condition of FIG.

Fig. 9A shows that the vertical axis (ωa/2πc) of the second photon energy band (2 _nd PB) satisfying the Bragg condition is converted into the wavelength λ _V in the vacuum, and the vertical axis is an integer multiple of the number of times (m = 3) : 3λ _V , horizontal axis: diagram of the photon band structure of ka/2π.

FIG. 9B based displays satisfy the Bragg conditions of a fourth photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 4: 3λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

FIG. 9C lines showed satisfying the Bragg condition of a fourth photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 5: 3λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Fig. 10A shows that the vertical axis (ωa/2πc) of the second photon energy band (2 _nd PB) satisfying the Bragg condition is converted into the wavelength λ _V in the vacuum, and the vertical axis is an integer multiple of the number of times (m = 4). : 4λ _V , horizontal axis: diagram of the photon band structure of ka/2π.

FIG. 10B based displays to satisfy the Bragg conditions of a fourth photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 5: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

FIG 10C based displays satisfy the Bragg conditions of a fourth photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 6: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

FIG. 10D based displays satisfy the Bragg conditions of a fourth photon energy band (4 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 7: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Fig. 11 is a view showing a calculation model (column) calculated by the finite time domain difference method (FDTD method).

Fig. 12 is a view showing a state in which the radiation pattern calculation parameters are calculated at intervals of 5° in the range of 0° θ θ ≦ 180° and 0° ≦ φ ≦ 360°, respectively.

Fig. 13 is a flow chart showing the flow of calculation by computer simulation in the embodiment.

Fig. 14 is a view showing the angular distribution of the radiation pattern when the number of times m = 3.

Fig. 15 is a view showing the angular distribution of the radiation pattern when the number of times m = 4.

Fig. 16 is a graph showing the angular distribution of the radiation pattern by selecting the R/a of the LEE increase and decrease rate of 300% or more and the number of times m at θ = 5° indicating the degree of light distribution.

Fig. 17 is a view showing a state in which TE light reflection by a photonic crystal is used.

18 is a photonic band gap (PBG) between 1 _st PB-2 _nd PB, 3 _rd PB-4 _th PB, 5 _th PB-6 _th PB, and 7 _th PB-8 _th PB as PBG1, respectively. PBG2, PBG3, PBG4, and a graph showing the relationship between R/a and PBG.

FIG 19 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V, and when m = 1 to the number and λ _V ka / 2π of A diagram of the photon energy band structure.

Figure 20 displays based photon satisfy the Bragg condition of the eighth band (8 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V, and when m = 1 to the number and λ _V ka / 2π of A diagram of the photon energy band structure.

Figure 21 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 5: 3λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Figure 22 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 6: 3λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Figure 23 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 6: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Figure 24 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integral multiple of the longitudinal axis 7: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Figure 25 displays based photon satisfy the Bragg condition of the sixth band (6 _th PB) of longitudinal axis (ωa / 2πc) in terms of the wavelength in vacuum of λ _V and is an integer multiple of 8 vertical axis: 4λ _V, and the horizontal axis: A diagram of the photonic band structure of ka/2π.

Fig. 26 is a view showing a calculation model (hole) calculated by the finite time domain difference method (FDTD method).

27(a) to 27(f) show the case where a periodic structure of a photonic crystal having a fine pattern of nm level is produced using a transfer technique based on nano-embossing lithography using two layers of resist. Figure.

Hereinafter, the form for carrying out the present invention will be described in detail with reference to the drawings. Further, the structure, constituent material, and periodic structure shape (column structure, pore structure, and the like) of the LED element in the embodiments described below are not limited thereto, and are within the range in which the effects of the present invention can be exhibited. It can be changed as appropriate. Further, the embodiment can be carried out as appropriate without departing from the scope of the invention. Again, for example A design program of a periodic structure, a mold processed according to the present invention, and the like are also included in the present invention.

An embodiment of the present invention provides a light-emitting element having a reflective film on a surface (side) of a GaN substrate and two structures including different refractive indices on a back surface (side) of the GaN substrate. The periodic structure of the photonic crystal, and the periodic structure of the photonic crystal described above, has high light extraction efficiency and excellent light distribution from the back surface of the GaN substrate.

(First embodiment)

First, a light-emitting element according to a first embodiment of the present invention will be described.

The periodic structure of the photonic crystal contains two structures having different refractive indices, and the periodic structural parameters, that is, the period a and the radius R are designed to satisfy the Bragg condition relationship with the wavelength λ. When the interface is complex, the periodic structure of each photonic crystal is an independently designed structure.

Fig. 1 is a cross-sectional view showing a configuration example of a light-emitting device of the embodiment (Fig. 1(a)) and a plan view (Fig. 1(b)) as viewed from the back side. The light-emitting element shown in Fig. 1 is a GaN substrate LED. The GaN substrate LED shown in FIG. 1( a ) has, for example, an Al reflective film 1 , an ITO transparent electrode 3 , a p-type GaN layer 5 , and a GaN active layer (light emitting layer) from the opposite side (surface side) to the GaN substrate. 7. An n-type GaN layer 11, a GaN substrate 15, and a photonic crystal structure (phc) 17. An AlGaN layer may also be present.

In this structure, the main light extraction surface is a flip chip structure on the back surface of the GaN substrate 15, and a photonic crystal structure 17 is formed on the back surface of the GaN substrate 15. As shown in FIG. 1(b), a photonic crystal structure (phc) 17 is formed on the back surface 15a of the GaN substrate 15, and includes a GaN pillar structure 17a and air 17b.

Here, if the radius of the GaN pillar structure 17a is R and the period is a, for example, the ratio of the period a to the radius R (R/a) is based on the transmission and reflection of light in the periodic structure of the wavelength λ. Focus on which one to optimize and determine the value.

For example, if the reflection of light at the interface is greater than the transmission, the R/a value is determined by focusing on the TE light. This is because the electric field of TE light is easily accumulated in the joint structure of the dielectric body which exists in parallel in the periodic structure plane, and when the periodic structural parameters and the design wavelength satisfy the Bragg condition, the electric scene will be due to Prague. Diffraction and reflection.

Conversely, if the ratio of the period a to the radius R (R/a) is such that the transmission of light at the interface is greater than the reflection, the R/a value is determined by focusing on the TM light. This is because the electric field of TM light is easy to accumulate in the dielectric point vertically existing in the periodic structure plane, and when the periodic structure parameter and the design wavelength satisfy the Bragg condition, the electric field surface will be diffracted by Bragg. The reflection, that is, the transmission relative to the periodic structural surface.

Further, each periodic structural parameter is subjected to the FDTD method by using the period a and the radius R determined from R/a in accordance with the number m of Bragg conditions, and the depth h of the periodic structure of 0.5 a or more. The result of the simulation analysis is configured such that the light extraction efficiency of the entire semiconductor light-emitting device having the wavelength λ is maximized. Here, the depth h of the periodic structure having a depth of 0.5 a or more may be a value whose upper limit is limited according to actual machining accuracy.

In the periodic structure of the photonic crystal of the present embodiment, the ratio (R/a) of the period a to the radius R is determined based on the photon energy band of the TM light so that the light transmission effect is good. Such a structural system refers to, for example, a structure (GaN column) in which a large refractive index (air or the like) is formed in a medium having a small refractive index, that is, a so-called column structure.

In the present embodiment, the optimization of the parameters of the periodic structure is for the purpose of transmission, and the transmitted light can be studied for TM light (see Fig. 2).

As shown in FIG. 2, it can be understood that the electric field of the TM light is apt to accumulate in the dielectric point vertically existing between the columnar rods (columns) 17a of the column structure, and the Bragg condition is satisfied at the average refractive index n _av , the period a, and the design wavelength λ. At the time of the electric field, the diffraction is caused by the Bragg diffraction, that is, the TM light system is transmitted with respect to the periodic structural surface (interface 15a) of the present embodiment.

The plane wave expansion method is an effective method for knowing the physical properties of TM photonic crystals. A photon energy band (PB) structure is obtained for the resolver. The equation of intrinsic value of TM light is derived from Maxwell's equation in the following manner.

Wherein E'=|k+G|E(G), ε: relative dielectric constant, G: inverse lattice vector, k: wave number, ω: number of cycles, c: speed of light, and E: electric field.

There are innumerable inverse lattice vectors (G), but G is taken as the minimum distance between the origin and the inverse lattice point, and G=±b1, ±b2, ±(b1) in the case of a triangular lattice photonic crystal. +b2) These six, as shown in Fig. 3, can obtain the first Brillouin region of the hexagon.

In Fig. 3, the points Γ, M, and K are referred to as symmetry points. Figure 4 shows the non-lattice band structure of the uniform medium in the region enclosed by the symmetry point, and Figure 5 shows the photonic band (PB) structure of the photonic crystal.

Fig. 5 is a scattering wave of each PB wavenumber vector k+G from 1st to 7th.

Moreover, since each of the PB systems is formed by reordering the eigenvalues from the low order of energy, it does not necessarily coincide with the wavenumber vector of the non-lattice photonic band.

As can be seen by comparing Fig. 4 with Fig. 5, in Fig. 5, a significant photonic band gap (PBG) can be observed at the symmetry point.

For example, at the point of the no-lattice state of Fig. 4, the solution is de-simplified, but the degeneracy is removed at the point of the photonic crystal structure of Fig. 5, and the standing wave is made of six waves. In the photonic crystal structure of Fig. 5, in the same manner, the two-fold degeneracy is removed at the M point, and the standing wave is generated by the two waves. At the K point, the three-fold degeneracy is released and the three waves are used to form the standing wave.

A group velocity anomaly (dω/dk=0) is generated at the symmetry points, resulting in a change in the direction of propagation of the light. Therefore, by focusing on the physical properties of light at each symmetry point of each photon energy band, a pointer for optimizing the light extraction efficiency or light distribution of the photonic crystal can be obtained.

To this end, focus on the photon energy band (PB) of the standing wave at the Γ point, M point, and K point. The reason is that the larger the refractive index difference at the interface, the more multiples will appear in the case of TM light. The reason for the above PBG.

An outline of the processing flow of the computer simulation for focusing on the above points is explained below.

Fig. 13 is a flow chart showing the flow of calculation of the computer simulation of the embodiment.

(Step S1)

In step S1, R/a (R: radius, a: period) is changed in steps of, for example, 0.01 in the range of 0.18 ≦ R / a ≦ 0.40.

(Step S2)

Since the scattered wave satisfying the Bragg condition corresponds to any of the photon energy bands (PB), the period a for transmitting the design wavelength λ is associated with the Bragg pattern. Here, the photon energy band of the eye is a scattering wave (k+G) satisfying the Bragg condition.

That is, in step S2, the average refractive index n _{av is} calculated from the refractive indices n ₁ , n ₂ , and R/a of the structure, and is substituted into the equation mλ/n _av = 2a of Prague, and is determined for each number m a and R.

Here n _av ² =n ₂ ² +(n ₁ ² -n ₂ ² )×(2 π / ) × (R / a) ² .

Further, according to the definition of the photonic crystal, the period a is close to the wavelength λ, and the period when the number of times m = 3 and 4 corresponds to the wavelength region.

For example, when R/a = 0.34 (m = 4), it can be calculated as follows.

If n ₁ = 2.50, n ₂ = 1.0

Then n _av ² =(2.50) ² +((2.50) ² -(1.0) ² )×(2 π / )×(0.34) ² =(1.79) ²

Therefore, n _av = 1.79. Substituting the number m=4, the wavelength in vacuum = 455 nm into the equation of Prague, a = 509 nm. Further, from R/a = 0.34, d = 346 nm can be obtained.

(Step S3)

In step S3, the dielectric coefficients ε ₁ and ε _{2 are} obtained from the determined R/a, the wavelength λ, the refractive indices n ₁ and n ₂ , and the photon energy band (PB) structure of the TM light is obtained by the plane wave expansion method. R/a corresponding to the number of maximum values of PBG1, PBG2, and PBG3, m=3 to 4, is a candidate for optimization.

6 shows the photonic band gap (PBG) between 1 _st PB-2 _nd PB, 3 _rd PB-4 _th PB, and 5 _th PB-6 _th PB as PBG1, PBG2, and PBG3, respectively, and shows R/a. Relationship with PBG.

As shown in Fig. 6, at R/a = 0.19, R/a = 0.23, and R/a = 0.32, the maximum value of each photonic band gap can be obtained. Since the size of the photonic band gap is correlated with the light extraction efficiency, the R/a system obtained from Fig. 6 is a powerful candidate for optimization regardless of the number of times.

(Step S4)

The vertical axis (ωa/2πc) of the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) satisfying the Bragg condition is converted into a wavelength λ _{V in} vacuum, which is obtained when the number of times m=1 Photonic band structure of λ _V and ka /2π. The vertical axis can be used as the ωa/2πc=a/λ _PhC transform (where λ _PhC is the wavelength in the photonic crystal (PhC)). Therefore, a ₁ = λ _V /2n _av is derived from λ _v = λ ₁ = a ₁ / (ωa / 2πc) × n _av and Bragg, that is, 1 × λ _V / n _av = 2a ₁ . The reason for selecting the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) is that the PBG1 and PBG2 are enlarged at 0.18 ≦R/a ≦ 0.40 as shown in FIG. At each symmetry point, a standing wave is generated by the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB), and then the direction of light propagation is changed.

Figures 7A, 7B show these situations. The second photon energy band (2 _nd PB) produces R/a in the standing wave at each symmetry point, which is the R/a which is in point or closest to the wavelength of 455 nm in vacuum. Therefore, if read from Fig. 7A, R/a = 0.37 at the defect, R/a = 0.21 at the M point, and R/a = 0.26 at the K point. In Fig. 7B, in the range of 0.18 ≦R/a ≦ 0.40, since either R/a is not close to the wavelength 455 nm in the vacuum, no standing wave is generated.

(Step S5)

First, research was conducted on R/a determined by the number m=3. As shown in FIG. 8A, the second photon energy band (2 _nd PB) of R/a=0.37 (number of times m=1) of step 4 generates a standing wave. The period of the number m=3 is 3 integer multiples of the period length of m=1, and the standing wave having three antinodes is generated because the phase is maintained. Therefore, λ ₃ = a ₃ / (ωa / 2πc) × n _av , a ₃ = 3λ _V /2n _av .

The period at m = 3 is three times the period at m = 1. Therefore, the wavelength of the vertical axis is also the wavelength λ _V × 3 (number of times m) in the vacuum.

Further, the R/a of the standing wave is R/a which is at or near the point of the wavelength × 3 = 1365 nm in the vacuum at each symmetry point, and is the same as the number of times m = 1 and becomes a defect (R/a =0.37), M point (R/a=0.21), and K point (R/a=0.26), which are candidates for optimization. Figure 9A shows the photonic band structure of the wavelength x 3 (number of times) and wave number in the vacuum of the second photon energy band (2 _nd PB).

On the other hand, when m=1, the number of cycles of the fourth photon energy band ( _4th PB) is higher than that of the second photon band ( _2nd PB) and is twice as weak. Moreover, no R/a in the range of 0.18 ≦R/a ≦ 0.40 does not generate standing waves. However, when the number of times m=3, the period length becomes larger in proportion to the number of times, and the standing wave is generated in the same phase at a certain R/a. As shown, a fourth photon R / a of the band 8B (4 _th PB) generates a standing wave condition, the length R of a line m = 1 / a of cycles 4 and 5 an integer multiple of an integer multiple of, in m The standing wave with 4 antinodes and 5 antinodes is generated in the period of =3.

Therefore, in order to find the R/a which is at the point of the wavelength × 3=1365 nm in the vacuum at each symmetry point, or the closest R/a, the fourth photon band of all the R/a obtained in the step S4 is obtained. (4 _th PB) is set to an integral multiple of those lines 4 shown in 9B, the integral multiple of the set 5 are shown in FIG. 9C. Among the four integer multiples are: Γ point (R/a=0.31), M point (R/a=0.31), and K point (R/a=0.36). Among the five integer multiples are: Γ (no match), M point (R/a = 0.18), and K point (R/a = 0.27), either of which is a candidate for optimization.

(Step S6)

When the number of times m=4, λ ₄ = a ₄ / (ωa / 2πc) × n _av , a ₄ = 4λ _V /2n _av . Figure 10A shows the photonic band structure for the wavelength and wavenumber in the vacuum of the second photon energy band (2 _nd PB). The R/a closest to the wavelength in the vacuum × 4 = 1820 nm at each symmetry point is the same as the number of times m = 1, but is the defect point (R / a = 0.37), M point (R / a = 0.21) , K point (R/a = 0.26). Further, a R / a photonic band of a fourth (4 _th PB) generates a standing wave condition of the system m = incident wavelength of 1 when integer multiples of 5, 6 integer multiple of an integer multiple of 7. Therefore, if R/a which is in point or closest to the wavelength in the vacuum at each symmetry point × 4 = 1820 nm is obtained, it is a defect point (R/a = 0.35) and M point at 5 integer multiples. (R/a=0.34). If the fourth longitudinal axis of the photonic band re-converted to the frequency when m = ωa 1 / 2πc, compared with FIG. 5 corresponds to the point K of the 4 _th PB (R / a = 0.40) (Figure 10B). At 6 integer multiples, it is a defect (R/a = 0.20), M point (R/a = 0.27), and K point (R/a = 0.31) (Fig. 10C). At 7 integer multiples, it is a defect (no match), M point (no match), and K point (R/a = 0.24) (Fig. 10D), either of which is a candidate for optimization.

(Step S7)

The light extraction efficiency ratio and the light distribution corresponding to the photonic crystal of R/a obtained in step S2 are all in the range of 0.18 ≦R/a ≦ 0.40, and the number of times is m=3. 4 Calculated by finite time domain difference method (FDTD method). Regarding the depth, an arbitrary value of 0.5 times or more of the maximum period a when the number m = 3 to 4 is selected.

Figure 11 shows the calculation model.

The flip chip structure is composed of an Al reflective film, an ITO transparent electrode, a p-GaN layer, a light-emitting layer, an n-GaN layer, and a GaN substrate. The light emitted by the light-emitting layer is mainly emitted from the back surface or the side wall of the GaN substrate toward the outside. The center wavelength is 455 nm and the degree of polarization is 0.94. A photonic crystal is formed on the back surface of the GaN substrate. When the output 1 is used as the output of the LED without photonic crystal and the output 2 is used as the output of the LED having the photonic crystal, the light extraction efficiency (LEE) increase and decrease rate is calculated as follows. That is, the LEE increase/decrease rate = (output 2 - output 1) / output 1 is calculated for the far field (Far Field) and the near field (Near Field). Further, the radiation pattern for verifying the light distribution is calculated in the far field.

As shown in FIG. 12, the electric field intensity E _{total of the} point P ₁ is defined as E _total =|Eθ| ² +|Eφ| ² . This electric field strength is proportional to the intensity of the light. Therefore, the radiation pattern can be obtained by calculating the electric field intensity at the point P ₁ in the range of 0° ≦ θ ≦ 180° and 0° ≦ φ ≦ 360° at intervals of 5°.

【Table 1】

Tables 1 and 2 show the results of simulations by FDTD method for each R/a at m=3 and m=4. The LEE increase/decrease rate (Far Field@455nm) refers to the increase and decrease rate of LED elements at a wavelength of 455 nm calculated at a far field. The LEE increase/decrease rate (Near Field@455nm) refers to the increase and decrease rate of LED elements at a wavelength of 455 nm calculated at the near field. The LEE increase/decrease rate (θ=5°) refers to the total output in the range of 0°≦φ≦360° at θ=5° of the radiation pattern, and the increase or decrease rate compared with the presence or absence of the photonic crystal. . The so-called photon energy band (PB) state shows the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) which are candidates for the optimized photonic crystal optimization in steps 3 to 6. The state of each symmetry point.

Further, Fig. 14 and Fig. 15 show the angular distribution of the radiation pattern for each order m. In the polar coordinates of the FDTD method, the calculation is performed in the θ direction and the φ direction in steps of 5°. At this time, the intensity of light of each area element on the polar coordinates is expressed by sin θd θdφ. However, since the area of the detector for measuring the light distribution is constant, there is a contradiction between the two due to the change in the angle θ. Therefore, here, the intensity of the vertical axis is expressed as the relative output per unit area. Regarding the horizontal axis, the output of the angle θ is expressed by integrating all of φ in the range of 0° ≦ φ ≦ 360°.

(Step S8)

Among the R/a and the number of times m from which the light extraction efficiency (LEE) increase/decrease rate is large, R/a and the number m of the light distribution properties corresponding to the target are selected. Therefore, it is necessary to determine the parameters of the photonic crystal optimization, namely diameter, period, and depth. R/a which is a candidate for photonic crystal optimization obtained in steps S3 to S6 is compared with R/a other than the aforementioned candidates in the range of 0.18 ≦ R/a ≦ 0.40. The result is an optimization candidate for R/a obtained in the steps of S3 to S6.

According to Tables 1 and 2, the LEE increase/decrease rate of the LED element is selected to be 65% or more, and the RE of the LEE increase/decrease rate of 300% or more, for example, when θ=5° indicating the light distribution quality is selected, The number of times m is shown in the distribution of the radiation pattern angles in Fig. 16. Further, the micropatterns of the shapes below the PSS (Patterned Sapphire Substrate) were simulated and compared using the FDTD method. Conical column with a 60° side wall angle (upper/ Lower/cycle/depth) = (267 nm / 1200 nm / 1800 nm / 800 nm) and arranged in a triangular lattice. From Fig. 16, it is clearly obtained that R/a which is a candidate for photonic crystal optimization is superior to other R/a or micron patterns, and light extraction efficiency and light distribution are good. In particular, the result of the best light distribution when the pattern of R/a=0.34 (the number of times m=4) is above θ=0°~15°. Therefore, when the processing from step S1 to step S8 is performed, the light extraction efficiency and the light distribution property of the photonic crystal can be easily optimized.

Further, in actuality, when determining the structure of the manufactured optical semiconductor element, it can be determined based on the value of optimization, but even if the value of the optimization itself is not used, the structure using the value close thereto is also in the present invention. Within the scope of the.

Further, the light of the LED is transmitted between the TE light and the TM light while being elliptically polarized. Therefore, the case of the TE light incident on the photonic crystal is examined as follows.

As shown in Fig. 17, the electric field of the TE light is easily accumulated between the columnar rods parallel to the plane of the photonic crystal, and the electric field is in the case where the average refractive index n _av , the period a, and the design wavelength λ satisfy the Bragg condition. The upper reflection is caused by the diffraction of Prague. The physical properties of the photonic crystal of TE light are resolved by obtaining the photonic band (PB) structure from the following Maxwell equation using the same procedure as the aforementioned TM light (steps S1 to S3).

Wherein ε: relative dielectric constant, G: inverse lattice vector, k: wave number, ω: number of cycles, c: speed of light, H: magnetic field.

The photonic band gap (PBG) between 1 _st PB-2 _nd PB, 3 _rd PB-4 _th PB, 5 _th PB-6 _th PB, and 7 _th PB-8 _th PB is set as PBG1, PBG2, respectively. PBG3, PBG4, the relationship between R/a and PBG is shown in FIG.

If compared with the PBG of TM light, there is no PBG1 and PBG2 in the TE light. Therefore, there is no standing wave in the photon energy bands, and the reflection effect of the TE light is weakened. Moreover, although PBG3 has PBG in the range of 0.28 ≦R/a ≦0.39, its size is compared with that of TM light PBG. very small. Although PBG4 has PBG in the range of 0.20 ≦R/a ≦ 0.25, its size is also very small. However, since PBG3 is small at R/a=0.34 and PBG4 at R/a=0.22, the maximum value can be obtained separately, so it is a strong candidate for optimization.

Secondly, the TM light and the same step S4, the sixth satisfy the Bragg conditions of photon energy band (6 _th PB) photonic band and the eighth (8 _th PB) is converted to a longitudinal axis of the wavelength in vacuum of λ _V, to the number of The photon band structure was obtained with m = 1 and is shown in Figs. 19 and 20. Since either R/a is not close to the wavelength of 455 nm in the vacuum, no standing wave is generated. Further, in FIGS. 21 to 25, the photon energy band structure in which the standing wave condition is satisfied is performed in the same manner as the TM light (steps S5 to S6) in terms of the number of times m=3 and the number of times m=4. A powerful candidate for optimization is that at m=3, it is a defect point (R/a=0.33) and a K point (R/a=0.36) at the integer multiple of the sixth photon energy band, at 6 integer multiples. It is the M point (R/a = 0.29); the eighth photon energy band has no match. Similarly, when m=4, it is a defect point (R/a=0.38) at the integer multiple of 6 of the sixth photon energy band, and a defect point (R/a=0.31) and M point (R/a) under 7 integer multiples. = 0.35), K point (R/a = 0.32), 8 integer points are M points (R / a = 0.29); the eighth photon energy band has no match.

The R/a system optimized by the analysis of TE light is reflected by the photonic crystal into the inside of the LED. However, since the energy of the standing wave is small due to the small size of each PBG, the reflection effect is higher than that of the TM light. The effect is weak. This case can also be understood from the fact that the results of the increase and decrease rates of the light extraction efficiency of the FDTD analyzed for the number m=3 and m=4 are all consistent. Further, since the light of the GaN-based blue LED which is crystal grown on the sapphire C plane is almost always polarized by TE, the polarization degree of the light source is also set to 0.94 in the analysis of the FDTD of the present embodiment. This is because the intensity of the TE light is 10 times or more that of the TM light, and in general, a photonic crystal (hole) which is advantageous for TE light is often formed. However, the analysis results show that the effect of increasing or decreasing the light extraction efficiency of the photonic crystal (column) is very high, so the structure of the photonic crystal is designed without the TE light or the TM light in response to the processing place of the light extraction surface. The importance.

Therefore, using the plane wave expansion method, the PBG of the TE light is formed as shown in FIG. The hole having the largest R/a = 0.40 was formed on the back surface of the GaN substrate, and the analysis of the increase and decrease rate of the light extraction efficiency was carried out by the FDTD method under the same conditions as the column. Among them, the Bragg condition is satisfied with respect to the design wavelength of 455 nm in the order of m=4, diameter=407 nm, period=508 nm, and depth=500 nm. The result of the increase or decrease rate of light extraction efficiency is 65%. This value is compared to the optimized column structure, and there is some degradation as indicated by the above.

Next, a method of manufacturing a photonic crystal structure will be described. The nanocompression mold has a superior technique of transferring a photonic crystal pattern of a mold over a large area onto an organic resist spin-coated on a substrate. Further, when the resin film mold is used, the substrate can be transferred even if the substrate is bent by several hundred micrometers. However, the organic resist used for the nano-molding mold is not necessarily sufficient in terms of the fluidity and the etching selectivity of the material which is the pattern-forming portion. Further, the pattern size of the mold is inconsistent with the size of the formed portion after etching. Therefore, in order to solve this problem, a process using a two-layer resist is carried out as follows.

That is, the process includes: a step of rotating and coating a substrate on the substrate to select a larger resist than a lower layer, and spin coating the upper resist on the underlying resist to have a fluidity and an oxygen resistance function; And the step of transferring the photonic crystal pattern on the upper layer, exposing the resist with the upper layer of the pattern to the oxygen plasma to impart oxygen resistance, and the patterned upper layer resist having the aforementioned oxygen resistance The agent is used as a mask to form a pattern of the underlying resist by oxygen plasma, and the photonic crystal is formed by dry etching the substrate by ICP plasma using the patterned underlying resist as a mask.

According to this method, by changing the film thickness of the underlying resist, it is possible to obtain an etching depth which is twice as large as the depth of the mold pattern (in the case of GaN). Further, by changing the oxygen plasma condition at the time of forming the mask using the upper resist under the resist, it is possible to adjust the diameter of the mold pattern by about 30%.

The following is a description of the more detailed manufacturing steps. In order to obtain good light extraction efficiency, it is necessary to form a process of a degree of nm as a calculation.

Therefore, according to the characteristics of utilizing both the fluidity and the etching selectivity ratio, In the transfer technique of the nano-mold lithography of the layer resist, the periodic structure of the photonic crystal having a fine pattern of a degree of nm is transferred to the back surface of the GaN substrate as an example as shown in FIG.

The design wavelength is λ, and a laminated structure including at least the Al reflective electrode 1, the p-type GaN layer 5, and the p-type GaN light-emitting layer 7 in the following order from the opposite side of the GaN substrate 15 is prepared, and is prepared for use in GaN. A mold of the photonic crystal periodic structure 17 is formed on the opposite side of the Al reflective electrode 1 of the substrate 15, and a resist layer is formed on the surface of the GaN substrate 15, and the structure of the mold is transferred, and the resist layer is masked from the GaN substrate. The 15th surface is etched to form a photonic crystal periodic structure 17. The process will be described below with reference to Fig. 27.

First, a mold for correctly reproducing a periodic structure optimized according to the implementation of the present invention on a GaN substrate was fabricated. As the mold, a mold made of a resin which can follow the deflection of the substrate as shown in Fig. 27(b) can be used.

Next, the organic underlayer resist having a large etching ratio to the GaN substrate is spin-coated at a thickness g. Moreover, the thickness g is selectively determined according to the etching selectivity ratio of the underlying resist of the GaN substrate. Thereafter, the ruthenium-containing upper resist having fluidity and oxygen resistance is spin-coated on the lower resist surface at a specific thickness (Fig. 27 (a)).

Next, the pattern of the mold was transferred onto the upper resist using a nanomolding apparatus (Fig. 27 (b)).

Next, the upper layer resist to which the pattern of the mold is transferred is exposed to the oxygen plasma to impart oxygen resistance and remove the residual film of the upper layer resist remaining in the nano-mold transfer. (Fig. 27(c)).

Next, the organic underlayer resist was etched by oxygen plasma using a resist having an oxygen-resistant upper layer as a mask to form a pattern mask for dry etching the GaN substrate (Fig. 27 (d)). Further, the pattern in FIG. 27 (e) described in the mask substrate side of the diameter d ₁ of the GaN-based conditions by adjusting the oxygen plasma and can be finely adjusted in the range of d ₁ of about 30%.

Using ICP plasma to dry-etch GaN substrates by pattern mask to form the best The periodic structure of the transformation (Fig. 27(e)).

In the case of the periodic structure of the pillar structure, the shape after etching is a trapezoid substantially d ₁ < d ₂ as shown in Fig. 27 (f), and the sidewall angle depends on the etching selectivity ratio of the organic underlying resist. Further, according to the present embodiment, when the thickness g of the organic underlayer resist is changed, the depth of the periodic structure of the photonic crystal formed on the dry-etched GaN substrate can be easily set to 1.5 times the depth of the mold. depth.

Further, when the diameter d ₁ is changed when the pattern mask is formed, the diameter of the periodic structure can be easily changed by 30%. This can replace the re-production of the mold, which helps to reduce the manufacturing time and cost of the mold, and thus becomes a significant advantage in the manufacturing cost of the semiconductor light-emitting element.

The processing and control can be realized by hardware processing of a CPU (Central Processing Unit) or a GPU (Graphics Processing Unit), an ASIC (Special Application Integrated Circuit) or an FPGA (Field Programmable Logic Gate Array).

In addition, in the above-described embodiment, the configuration and the like shown in the drawings are not limited, and can be appropriately changed within the range in which the effects of the present invention can be exerted. Others can be appropriately modified and implemented without departing from the scope of the invention.

Further, the constituent elements of the present invention can be arbitrarily selected and selected, and the invention having the configuration of the selection is also included in the inventors.

Further, a program for realizing the functions described in the embodiment can be recorded on a computer-readable recording medium, and each part can be processed by reading and executing a program recorded on the recording medium by the computer system. In addition, the term "computer system" as used herein refers to a hardware including an OS or a peripheral device.

In addition, if the "computer system" is used in the case of the WWW system, it is also the environment (or display environment) that also includes the home page.

In addition, the term "computer-readable recording medium" means a removable medium such as a floppy disk, a magneto-optical disk, a ROM, a CD-ROM, or a hard disk built in a computer system. Memories. In addition, the term "computer-readable recording medium" refers to a program that dynamically maintains a program for a short period of time, including a communication line when a program is transmitted via a communication line such as the Internet or a telephone line. It also includes the program that keeps the program for a certain period of time like the volatile memory inside the server or client computer system in this case. In addition, the program may be used to implement one of the functions described above, and may also be implemented by combining with a program already recorded in a computer system. At least a part of the function can also be realized by a hardware such as an integrated circuit.

All publications, patents, and patent applications cited in this specification are hereby incorporated by reference in their entirety herein

[Industrial availability]

The present invention can be utilized as a semiconductor light emitting element.

1‧‧‧Al reflective film/Al reflective electrode

3‧‧‧ITO transparent electrode

5‧‧‧p-type GaN layer

7‧‧‧GaN active layer (light-emitting layer) / p-type GaN light-emitting layer

11‧‧‧n-type GaN layer

15‧‧‧GaN substrate

15a‧‧‧Back/Interface

17‧‧‧Photonic crystal structure (phc)/photonic crystal structure/photonic crystal periodic structure

17a‧‧‧GaN column structure/column structure rod (column)

17b‧‧‧air

A‧‧ cycle

H‧‧‧depth

R‧‧‧ Radius

Claims (13)

A semiconductor light-emitting device having a reflective film on a surface (side) of a GaN substrate and a photonic crystal periodic structure including two structures having different refractive indices on a back surface (side) of the GaN substrate, and the photonic crystal period Sexual structure: the design wavelength λ _{V in} vacuum and the parameters of the periodic structure, ie the period a and the radius R satisfy the Bragg condition, in the range of R/a from 0.18 to 0.40, in the photon band structure of the TM light There are 2 photonic band gaps within the four-photon energy band (4 _th PB). The semiconductor light-emitting element of claim 1, wherein the R/a system has the number m=3 or 4 as a value corresponding to a maximum value of each photonic band gap. The semiconductor light-emitting device of claim 1, wherein the R/a system has the number of times m=3 or 4, and when the vertical axis (ωa/2πc) of the photonic band structure is converted into a wavelength λ _V in a vacuum, The symmetry point of the second photon energy band (2 _nd PB) is any point at the Γ point, M point, and K point, and is at or closest to the wavelength λ _V × m in the vacuum. The semiconductor light-emitting device of claim 1, wherein the R/a system has the number m=3, the wavelength λ _V × 3 in the vacuum of the longitudinal axis (ωa/2πc) of the photonic band structure, and the fourth photon band (4 _th PB) is set to an integral multiple of 4 and 5 are each an integral multiple of a fourth photon energy with a point of symmetry on either of (4 _th PB) to the point of contact or closest value. The semiconductor light-emitting device of claim 1, wherein the R/a system has the number m=4, the wavelength λ _V × 4 in the vacuum of the longitudinal axis (ωa/2πc) of the photonic band structure, and the fourth photon band (4 _th PB) is set to an integer multiple of 5, 6 integer multiple of an integer multiple of each of the fourth photon energy band 7 (4 _th PB) of any point on a symmetrical point of contact or closest value. The semiconductor light-emitting device according to any one of claims 1 to 5, wherein the parameters of each periodic structure are calculated by the FDTD method for each selected R/a and a depth of 0.5 a or more. The photonic crystal of h is finally determined by the method of optimizing light extraction efficiency and light distribution. The semiconductor light-emitting device according to any one of claims 1 to 6, wherein the structural system forms a structure having a large refractive index in a medium having a small refractive index. A method for calculating a parameter of a periodic structure of a photonic crystal, characterized in that it is a parameter calculation method for a periodic structure of a photonic crystal of a semiconductor light-emitting element according to any one of claims 1 to 7, and the method has the following steps: , which is the parameter of the tentative periodic structure, that is, the ratio of the period a to the radius R of the structure (R/a); the second step, which is the refractive index n ₁ , n ₂ of the respective structures from the structure, and the like Calculating the average refractive index n _av with the refractive index and the above R/a, and substituting it into the Bragg conditional expression, and obtaining the period a and the radius R for the number of times m=3 and m=4; the third step is by using The photonic band structure of the TM light is analyzed from the plane wave expansion method of the dielectric constants ε ₁ and ε ₂ of the respective structures obtained by the above-mentioned R/a and the above-mentioned wavelength λ and the above-mentioned refractive indices n ₁ and n ₂ ; a step of converting the longitudinal axis (ωa/2πc) of the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) of the TM light into a wavelength λ _V in the vacuum, the number of times m= 1 obtain the photonic band structure of λ _V and ka/2π; the 5th and 6th steps, the number of times m=3 and m=4, find the second photon band of TM light (2 _nd At a point symmetry each wavelength in vacuum of λ _V × m PB) and a fourth photonic band (4 _th PB) or closest to the contact point of the R / a, and set the optimal candidate And the seventh step, which is for the total number of R/a in the range of 0.18 ≦R/a ≦ 0.40, m=3 and 4 using the finite time domain difference method (FDTD method), and the calculation corresponds to the aforementioned R/a In the photonic crystal, the light extraction efficiency is increased or decreased, and the light distribution property is selected, and the depth system is selected from any of the maximum period a by 0.5 times or more. A method for calculating a parameter of a periodic structure of a photonic crystal, characterized in that it is a parameter calculation method for a periodic structure of a photonic crystal of a semiconductor light-emitting element according to any one of claims 1 to 7, and the method has the following steps: , which is the parameter of the tentative periodic structure, that is, the ratio of the period a to the radius R of the structure (R/a); the second step, which is the refractive index n ₁ , n ₂ of the respective structures from the structure, and the like Calculating the average refractive index n _av with the refractive index and the above R/a, and substituting it into the Bragg conditional expression, and obtaining the period a and the radius R for the number of times m=3 and m=4; the third step is by using The photon energy band structure of the TM light is analyzed from the plane wave expansion method of the dielectric constants ε ₁ and ε ₂ of the respective structures obtained by the above R/a, the wavelength λ, and the refractive indices n ₁ and n ₂ ; a step of converting the longitudinal axis (ωa/2πc) of the second photon energy band (2 _nd PB) and the fourth photon energy band (4 _th PB) of the TM light into a wavelength λ _V in the vacuum, the number of times m= 1 Obtaining the photonic band structure of λ _V and ka/2π; the fifth and sixth steps, the number of times m=3 and m=4, and obtaining the second photon band of TM light (2 _nd PB) At a point symmetry each wavelength in vacuum of λ _V × m or closest to a point of contact R / a, and set as the best candidate of the photonic band and the fourth (4 _th PB) of; the first In the seventh step, the photon crystal corresponding to the aforementioned R/a is calculated by using the finite time domain difference method (FDTD method) for all R/a in the range of 0.18 ≦R/a ≦ 0.40. The light extraction efficiency is increased or decreased, and the light distribution is selected, and the depth is m=3 to 4, and any value of 0.5 times or more of the maximum period a is selected; and the eighth step is the self-light extraction efficiency (LEE) Among the R/a and the number of times m having a large increase/decrease ratio, the R/a and the number m of the light distribution of the target are selected, and the diameter, the period, and the depth are determined, and the third step to the sixth step will be performed. The R/a of the candidate for photonic crystal optimization obtained in the step is compared with other R/a to select a parameter having a good light distribution property. The semiconductor light-emitting element of claim 1, wherein the photonic crystal periodic structure is processed using a transfer technique using nano-compression lithography. The semiconductor light-emitting element of claim 10, wherein the transfer of the periodic structure of the photonic crystal by the nano-embossing lithography is performed by coating a structure of the object to be processed with a relatively large underlying resist. And a transfer technique of a two-layer resist method having a layer of resist having fluidity and oxidation resistance coated thereon. A method of manufacturing a semiconductor light-emitting device, comprising: a step of preparing a laminated structure having a design wavelength of λ and sequentially including a reflective electrode and a p-type GaN light-emitting layer on a side opposite to a surface of the GaN substrate; a step of preparing a mold for forming a periodic structure of a photonic crystal on a side opposite to the reflective electrode layer of the GaN substrate; forming a resist layer on the surface of the GaN substrate, and transferring the structure of the mold And the step of forming a photonic crystal periodic structure by etching the surface of the GaN substrate with the resist layer as a mask. The method of manufacturing a semiconductor light-emitting device according to claim 12, wherein the step of forming a resist layer on the surface of the GaN substrate and transferring the structure of the mold has a method of using a two-layer resist on the surface of the GaN substrate a step of dry etching, wherein the two resist layers are a first resist layer having a high fluidity, and a second resist layer having a higher etching selectivity than the first resist layer; and The structure of the above mold is transferred to the first resist layer by nano-mold lithography And the step of forming the photonic crystal periodic structure by sequentially etching the GaN substrate surface by using the resist layer as a mask: etching the first resist layer and the second resist layer until the foregoing 2, the resist layer is exposed, and the pattern convex portion of the first resist layer is also etched together; and the second resist layer is used as a mask, and the GaN substrate surface is sequentially etched to form a photonic crystal periodic structure The steps.