Surface-emitting laser element and method for manufacturing the surface-emitting laser element

Abstract

To provide a photonic crystal surface light emitting laser in which flatness and crystallinity of an active layer formed on a multi-lattice photonic crystal layer are high, light extraction efficiency is high, and oscillation operation can be performed with low threshold current density and high quantum efficiency, and a method for manufacturing the same.SOLUTION: A surface light emitting laser element has: a first guide layer formed on a c-plane of a group III nitride semiconductor and having a photonic crystal layer having holes arranged with two-dimensional periodicity in a plane parallel to the layer and a buried layer formed on the photonic crystal layer to close the holes; an active layer formed on the first guide layer; and a second guide layer formed on the active layer. A hole set including at least a main hole and a sub-hole having a size smaller than that of the main hole is disposed at each of square lattice points in a plane parallel to the photonic crystal layer. The main hole has a regular hexagonal columnar shape, a long hexagonal columnar shape, or a long cylindrical shape having a long axis parallel to a <11-20>axis.SELECTED DRAWING: Figure 3

Description

[Technical Field]

[0001] The present invention relates to a surface-emitting laser element and a method for manufacturing the same, and more particularly to a photonic crystal surface-emitting laser element and a method for manufacturing the same. [Background technology]

[0002] In recent years, development of photonic-crystal surface-emitting lasers using photonic crystals (PC) has been progressing.

[0003] For example, Patent Document 1 describes a two-dimensional photonic crystal surface-emitting laser light source having a two-dimensional photonic crystal in which a plate-shaped base material is periodically filled with a large number of modified refractive index area assemblies, each of which is composed of a plurality of regions having a refractive index different from that of the base material and at least two of which have thicknesses different from each other. It is disclosed that this configuration reduces the symmetry in a plane parallel to the base material compared to a two-dimensional photonic crystal in which cylindrical modified refractive index areas are periodically arranged, thereby making it possible to suppress a decrease in laser light extraction efficiency due to cancellation of antisymmetric modes caused by interference.

[0004] When a burying layer is grown on a two-dimensional photonic crystal in which a large number of such voids are periodically arranged within the crystal plane, the surface of the burying layer becomes rough, which causes a problem of deteriorating the quality of the active layer grown on the burying layer. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 4294023 Summary of the Invention [Problem to be solved by the invention]

[0006] As described above, in photonic crystal surface emitting lasers, the surface of the burying layer in which the two-dimensional photonic crystal layer is buried becomes rough, which causes a problem of deteriorating the quality of the active layer formed on the burying layer.

[0007] Furthermore, the inventors of the present application have found that when a two-dimensional photonic crystal in which sets of air holes of different sizes are periodically arranged is embedded in an embedding layer, the surface of the embedding layer becomes rougher than in the case of a two-dimensional photonic crystal consisting of air holes of a single size.

[0008] In particular, they found that in the process of forming the buried layer, the shape of the voids changes due to mass transport, and the shape changes of the voids cause the shape changes of adjacent voids to interfere with each other, resulting in unevenness on the surface of the buried layer.

[0009] The present invention has been made in view of the above points, and aims to provide a photonic crystal surface-emitting laser having a two-dimensional photonic crystal (hereinafter also referred to as a multi-lattice photonic crystal) configured by arranging a plurality of air holes of different sizes at lattice points, with the plurality of air holes being periodically arranged in groups, and in which the flatness of the surface of the embedding layer in which the multi-lattice photonic crystal is embedded is greatly improved, and a method for manufacturing the same.

[0010] Another object of the present invention is to provide a photonic crystal surface-emitting laser that has an active layer formed on a multi-lattice photonic crystal layer with high flatness and crystallinity, has high light extraction efficiency, and is capable of oscillating at a low threshold current density and high quantum efficiency, and a method for manufacturing the same. [Means for solving the problem]

[0011] A surface-emitting laser element according to one embodiment of the present invention is a surface-emitting laser element made of a group III nitride semiconductor, a first guide layer including: a photonic crystal layer formed on a c-plane of a group III nitride semiconductor and having holes arranged with two-dimensional periodicity in a plane parallel to the layer; and a burying layer formed on the photonic crystal layer and closing the holes; an active layer formed on the first guide layer; a second guide layer formed on the active layer, a hole set including at least a main hole and a sub-hole having a size smaller than that of the main hole is arranged at each of the square lattice points in a plane parallel to the photonic crystal layer, The main holes have a regular hexagonal prism shape, an elongated hexagonal prism shape, or an elongated cylindrical shape with their major axes parallel to the <11-20> axis.

[0012] A method for manufacturing a surface-emitting laser element according to another embodiment of the present invention includes the steps of: forming a guide layer on a c-plane of a group III nitride semiconductor; forming an etching mask on the guide layer, the etching mask having an opening set including at least a main opening and a sub-opening having a size smaller than that of the main opening at each square lattice point; etching the guide layer using the etching mask to form main holes and sub-holes; performing crystal growth including mass transport to form a buried layer that closes the openings of the main holes and sub-holes, thereby forming a multi-lattice photonic crystal layer in which a hole set including a main hole and a sub-hole smaller in size than the main hole is arranged at each of the square lattice points; forming a semiconductor layer including an active layer on the multi-lattice photonic crystal layer, The main holes are characterized by having a regular hexagonal prism shape, an elongated hexagonal prism shape, or an elongated cylindrical shape with the major axis parallel to the <11-20> axis. [Brief explanation of the drawings]

[0013] [Figure 1A] 1 is a cross-sectional view schematically illustrating an example of the structure of a photonic crystal laser (PCSEL) 10. FIG. [Figure 1B] 1B is an enlarged cross-sectional view schematically showing photonic crystal layer 14P and air hole pairs 14K arranged in photonic crystal layer 14P in FIG. 1A. FIG. [Figure 2A] FIG. 2 is a plan view schematically showing the upper surface of the photonic crystal laser 10. [Figure 2B] 1B is a cross-sectional view schematically showing a cross section of photonic crystal layer 14P in a plane parallel to n-guide layer 14 (cross section AA in FIG. 1B). [Figure 2C] FIG. 2 is a plan view schematically showing the bottom surface of photonic crystal laser 10. [Figure 3] FIG. 10 is a top view schematically showing a resist in which pairs of openings, each consisting of an oval main opening K1 and a sub-opening K2, are two-dimensionally arranged in a square lattice pattern within the plane. [Figure 4] 1 is an SEM image of a GaN surface in which holes 14H1 and 14H2 are formed. [Figure 5] 10 is an SEM image of the upper surface of the guide layer, showing the shapes of main holes 14K1 and sub-holes 14K2 in this example. [Figure 6A] 6 is an SEM image showing a cross section taken along line AA in FIG. 5. [Figure 6B] 6 is an SEM image showing a cross section taken along line BB in FIG. 5. [Figure 7] 1 is an SEM image showing cylindrical holes CH formed in a GaN surface portion in Comparative Example 1. [Figure 8A] FIG. 1 is a graph showing the IL characteristics of the PCSEL device 10 of Example 1 and the PCSEL device of Comparative Example 1. [Figure 8B] FIG. 1 shows the emission spectra of the PCSEL device 10 of Example 1 and the PCSEL device of Comparative Example 1 near the threshold current. [Figure 9A] 10 is a top SEM image showing a main hole 14H1 and a sub-hole 14H2 of a structure (structure A) in which a main hole and a sub-hole are formed as in Example 1. [Figure 9B] 10 is a top SEM image showing a main hole CH1 and a sub-hole CH2 of Comparative Example 2 (structure B). [Figure 10A] 10 is an AFM image showing the surface morphology of the buried layer after filling the main voids and sub-voids in the case of Structure A (Example 2). [Figure 10B] 10 is an AFM image showing the surface morphology of the buried layer after filling the main voids and sub-voids in the case of Structure B (Comparative Example 2). [Figure 11A]FIG. 10 is a top view schematically showing the change in shape of a hole in the process of forming a buried layer in the case of Structure A (Example 2). [Figure 11B] FIG. 10 is a top view schematically showing the change in shape of a hole in the process of forming a buried layer in the case of Structure B (Comparative Example 2). [Figure 12A] 10 is a graph showing the cavity loss αn in the vertical direction when the relative position Δx, Δy (Δx=Δy) of the sub-hole 14K2 with respect to the main hole 14K1 is changed from 0.0PC to 0.5PC in the structure of Example 1. [Figure 12B] 10 is a graph showing the horizontal cavity loss αp when the relative position Δx, Δy (Δx=Δy) of the sub-hole 14K2 with respect to the main hole 14K1 is changed from 0.0PC to 0.5PC in the structure of Example 1. [Figure 12C] 10 is a graph showing Rn, which is the ratio of the vertical cavity loss αn to the total cavity loss (αp+αn). [Figure 13] FIG. 1 is a diagram showing the photonic band structure near the Γ point of a square lattice photonic crystal. [Figure 14] 10 is a graph showing the threshold gain (resonator loss) of each mode obtained from coupled-wave theory when Δx and Δy are changed in Example 1. [Figure 15] 3A and 3B are diagrams schematically showing the refractive index, carrier density, and photon density of a current injection region. [Figure 16A] 10 is a diagram showing the frequency of the photonic band edge in the vicinity of the current injection region in the cases of band edge modes A and B. FIG. [Figure 16B] 10 is a diagram schematically showing the frequency of the photonic band edge in the vicinity of the current injection region in the cases of band edge modes C and D. FIG. [Figure 17A] This is a diagram showing the refractive index, carrier density, and photon density in the current injection region when oscillating in band edge modes A and B. The solid and dashed lines show the cases when the photonic band effect is taken into account and when it is not, respectively. [Figure 17B]The graph shows the refractive index, carrier density, and photon density in the current injection region when oscillating in band edge modes C and D. The solid and dashed lines show the cases when the photonic band effect is taken into account and when it is not, respectively. [Figure 18] 1 is an SEM image of a GaN surface in which holes 14H1 and 14H2 are formed. [Figure 19A] 10 is an SEM image of the upper surface of the guide layer, showing the hole shapes of main holes 14K1 and sub-holes 14K2 in Example 3. [Figure 19B] 19B is an SEM image showing a cross section taken along line AA in FIG. 19A. [Figure 19C] 19B is an SEM image showing a cross section taken along line BB in FIG. 19A. [Figure 20A] FIG. 10 is a graph showing the IL characteristics of the PCSEL device 10 of Example 3 and the PCSEL device of Comparative Example 1. [Figure 20B] FIG. 1 shows the emission spectra of the PCSEL device 10 of Example 3 and the PCSEL device of Comparative Example 1 near the threshold current. [Figure 21A] FIG. 10 is a graph showing the vertical cavity loss αn versus d (the relative position of the subhole to the main hole). [Figure 21B] FIG. 10 is a diagram showing the horizontal cavity loss αp versus the relative position d. [Figure 21C] FIG. 1 shows the dependence of Rn on the relative position d. [Figure 21D] 10 is a graph showing the threshold gain (resonator loss) of each mode obtained from coupled wave theory when Δx and Δy (relative position d) are changed in Example 3. [Figure 22A] FIG. 10 is a graph showing Rn versus the hole filling ratio FF1 / FF2. [Figure 22B] FIG. 10 is a graph showing the sum of the cavity losses (αn+αp) in the vertical and horizontal directions relative to the hole filling factor ratio FF1 / FF2. DETAILED DESCRIPTION OF THE INVENTION

[0014] In the following, preferred embodiments of the present invention will be described, but these may be modified and combined as appropriate. In the following description and accompanying drawings, substantially the same or equivalent parts are designated by the same reference numerals. [Photonic crystal surface-emitting laser structure] A photonic crystal surface-emitting laser (hereinafter also referred to as PCSEL) is an element that has a resonator layer in a direction parallel to the semiconductor light-emitting structure layers (n-guide layer, light-emitting layer, p-guide layer) that constitute the light-emitting element, and emits coherent light in a direction perpendicular to the resonator layer.

[0015] Meanwhile, distributed Bragg reflector (DBR) lasers, which have a pair of resonator mirrors (Bragg reflectors) sandwiching a semiconductor light-emitting structure layer, are known, but photonic crystal surface-emitting lasers (PCSELs) differ from DBR lasers in the following respects: In a photonic crystal surface-emitting laser (PCSEL), light waves propagating in a plane parallel to the photonic crystal layer are diffracted by the diffraction effect of the photonic crystal to form a two-dimensional resonance mode, and are also diffracted in a direction perpendicular to the parallel plane. In other words, the light extraction direction is perpendicular to the resonance direction (in the plane parallel to the PC layer).

[0016] 1A is a cross-sectional view schematically illustrating an example of the structure (first PCSEL structure) of a photonic crystal laser device (PCSEL device) 10. As shown in FIG. 1A, a semiconductor structure layer 11 is formed on a substrate 12. The semiconductor structure layer 11 is made of a hexagonal nitride semiconductor. The semiconductor structure layer 11 is made of, for example, a GaN-based semiconductor.

[0017] More specifically, a semiconductor structure layer 11, that is, an n-clad layer (first clad layer of a first conductivity type) 13, an n-guide layer (first guide layer) 14, an active layer 15, a p-guide layer (second guide layer) 16, an electron barrier layer (EBL: Electron Blocking Layer) 17, a p-clad layer (second clad layer of a second conductivity type) 18, and a p-contact layer 19 are formed in this order on a substrate 12. Note that, although a case will be described in which the first conductivity type is n-type and the second conductivity type, which is the opposite conductivity type to the first conductivity type, is p-type, the first conductivity type and the second conductivity type may also be p-type and n-type, respectively.

[0018] The n-guiding layer 14 is made up of a lower guiding layer 14A, a photonic crystal layer (air hole layer or PC layer) 14P, and a burying layer 14B. The burying layer 14B is made up of a first burying layer 14B1 and a second burying layer 14B2.

[0019] In this specification, "n-" and "p-" mean "n-side" and "p-side," respectively, and do not necessarily mean that they have n-type or p-type. For example, an n-guide layer refers to a guide layer provided on the n-side of the active layer, and may be an undoped layer (or i-layer).

[0020] The n-cladding layer 13 may be composed of multiple layers, not just a single layer. In this case, all layers do not need to be n-layers (n-doped layers), and may include undoped layers (i-layers). The same applies to the guide layer 16 and the p-cladding layer 18.

[0021] Although the specific and detailed semiconductor layer configuration of photonic crystal laser device 10 has been described above, this is merely one example of the device structure. Essentially, it is sufficient that the device has a first semiconductor layer (or guide layer) having photonic crystal layer 14P, a second semiconductor layer (or guide layer), and an active layer (light-emitting layer) sandwiched between these layers, and is configured to emit light when a current is injected into the active layer.

[0022] For example, a photonic crystal laser element does not necessarily have to have all of the semiconductor layers described above, and may alternatively have various semiconductor layers (e.g., hole barrier layers, light confinement layers, current confinement layers, tunnel junction layers, etc.) for improving element characteristics.

[0023] An n-electrode (cathode) 20A is formed on the back surface of the substrate 12, and a p-electrode (anode) 20B is formed on the top surface of the p-contact layer 19. The side surfaces of the semiconductor structure layer 11 and the side surfaces of the upper part of the substrate 12 are covered with an insulating film 21 such as SiO2. The side surfaces of the p-electrode 20B and the surface of the p-contact layer 19 are also covered with the insulating film 21 so as to cover the edge of the top surface of the p-electrode 20B.

[0024] Light emitted directly from the photonic crystal layer (PC layer) 14P (directly emitted light Ld) and light emitted from the photonic crystal layer 14P and reflected by the p-electrode 20B (reflected emitted light Lr) are emitted to the outside from the light emission region 20L on the back surface of the substrate 12.

[0025] 1B is an enlarged cross-sectional view schematically showing photonic crystal layer 14P and air hole pairs 14K arranged in photonic crystal layer 14P in FIG. 1A. Air hole pairs 14K (main air holes 14K1 and sub-air holes 14K2) are formed in a crystal growth plane (semiconductor layer growth plane), i.e., in a plane (cross section AA in the figure) parallel to n-guide layer 14, with a period PC in the shape of, for example, a square lattice, and air hole pairs 14K are two-dimensionally arranged at square lattice point positions and embedded in n-guide layer 14.

[0026] FIG. 2A is a plan view schematically showing the top surface of photonic crystal laser (PCSEL) 10, FIG. 2B is a cross-sectional view schematically showing a cross section of photonic crystal layer (PC layer) 14P in a plane parallel to n-guide layer 14 (cross section AA in FIG. 1B), and FIG. 2C is a plan view schematically showing the bottom surface of photonic crystal laser (PCSEL) 10.

[0027] As shown in Fig. 2B, in photonic crystal layer 14P, air hole pairs 14K are periodically arranged within, for example, a rectangular air hole formation region 14R. As shown in Fig. 2C, n-electrode (cathode) 20A is provided as a ring-shaped electrode outside air hole formation region 14R so as not to overlap with air hole formation region 14R when viewed perpendicularly to photonic crystal layer 14P. The region inside n-electrode 20A is light emission region 20L. Also provided is bonding pad 20C that is electrically connected to n-electrode 20A and for connecting a wire for external power supply. [Example]

[0028] 1. Fabrication process of photonic crystal laser (PCSEL) 10 The following describes in detail the steps for fabricating the PCSEL device 10. Metalorganic Vapor Phase Epitaxy (MOVPE) was used as the crystal growth method, and the semiconductor structure layer 11 was grown on the growth substrate 12 by normal pressure (atmospheric pressure). In the steps described below, Sn means step n.

[0029] Furthermore, the layer thickness, carrier concentration, Group 3 (Group III) and Group 5 (Group V) raw materials, temperature, etc. shown below are merely examples unless otherwise specified. [S1: Board preparation process] We prepared GaN single crystals with a "+c" plane as the primary surface, which is the (0001) plane with Ga atoms arranged at the top surface. The primary surface can be exactly aligned, or the substrate can be offset by up to 1° along the m-axis. For example, substrates offset by up to 1° along the m-axis can achieve mirror-finish growth under a wide range of growth conditions.

[0030] The substrate surface (back surface) on which the light emission region 20L is provided, facing the main surface, is the "-c" plane, which is the (000-1) plane with N atoms arranged on the outermost surface. The -c plane is resistant to oxidation and is therefore suitable as a light extraction surface.

[0031] In this example, an n-type GaN single crystal was used as the GaN substrate 12. The n-type GaN substrate 12n functions as a contact layer with the electrode. [S2: n-clad layer formation process] On the +c-plane GaN substrate 12, an n-type Al clad layer 13 having an Al composition of 4% was formed. 0.04 Ga 0.96 The N layer was grown to a thickness of 2 μm. The AlGaN layer was grown by supplying trimethylgallium (TMG) and trimethylaluminum (TMA) as group III atom sources to a GaN substrate heated to 1100°C.

[0032] Carrier doping was performed by simultaneously supplying silane (SiH4) with the above-mentioned raw materials (Si doping). At this time, the carrier concentration at room temperature was approximately 4 × 10 17 cm -3 It was. [S3a: Lower guide layer + hole preparation layer formation process] Subsequently, TMG was supplied and n-type GaN was grown to a thickness of 250 nm as a preparatory layer for the n-guide layer 14. Silane (SiH4) was supplied at the same time as in the AlGaN layer for carrier doping. The carrier concentration at this time was approximately 4 × 10 17 cm -3 It was.

[0033] This growth layer is a preparation layer for forming a layer consisting of lower guide layer 14A and photonic crystal layer 14P.

[0034] In the following, for ease of explanation and understanding, the substrate 12 on which such a growth layer is formed (substrate with growth layer) may be simply referred to as a substrate. [S3b: Hole and void formation process] After forming the above preparatory layer, the substrate was removed from the chamber of the MOVPE apparatus, and fine holes were formed on the surface of the growth layer. More specifically, after the substrate was washed to obtain a clean surface, a silicon nitride film (Si x N y) was formed using plasma CVD. An electron beam lithography resist was applied on top of this by spin coating, and the resist was placed in an electron beam (EB) lithography system to pattern a two-dimensional periodic structure.

[0035] As shown in Figure 3, a pattern was performed in which pairs of apertures, each consisting of an oval-shaped main aperture K1 and a sub-aperture K2 smaller than the main aperture K1, were two-dimensionally arranged in the resist plane in a square lattice pattern with a period PC of 164 nm. For clarity of the drawing, the apertures are shown hatched.

[0036] More specifically, the main apertures K1 are arranged in a square lattice pattern with their centers of gravity CD1 in two mutually orthogonal directions (x direction and y direction) at a period PC=164 nm, and the sub-apertures K2 are also arranged in a square lattice pattern with their centers of gravity CD2 in the x direction and y direction at a period PC=164 nm.

[0037] The major axes of the main aperture K1 and the sub aperture K2 are parallel to the <11-20> direction of the crystal orientation, and the minor axes of the main aperture K1 and the sub aperture K2 are parallel to the <1-100> direction.

[0038] Furthermore, the center of gravity CD2 of the sub-aperture K2 is spaced apart from the center of gravity CD1 of the main aperture K1 by Δx and Δy. Here, Δx=Δy. That is, the center of gravity CD2 of the sub-aperture K2 is spaced apart from the center of gravity CD1 of the main aperture K1 in the <1-100> direction. Specifically, the center-of-gravity distance Δx in the x direction and the center-of-gravity distance Δy in the y direction were 65.6 nm (= PC × 0.4).

[0039] The main opening K1 had a major axis of 125 nm and a minor axis of 50 nm, with a ratio of the major axis to the minor axis (major axis / minor axis) of 2.50, and the sub-opening K2 had a major axis of 57.5 nm and a minor axis of 50 nm, with a ratio of the major axis to the minor axis of 1.15.

[0040] After developing the patterned resist, Si is etched using an ICP-RIE (Inductive Coupled Plasma - Reactive Ion Etching) device. x N yThe film was selectively dry-etched. As a result, main openings K1 and sub-openings K2 arranged in a square lattice pattern with a period of 164 nm were formed in the Si x N y formed to penetrate the membrane.

[0041] The period (hole spacing) PC was calculated as PC=λ / n=164 nm, with the oscillation wavelength (λ) set to 410 nm and the refractive index (n) of GaN set to 2.5.

[0042] Next, the resist is removed and the patterned Si x N y Using the film as a hard mask, holes were formed in the GaN surface. The GaN was dry-etched in the depth direction using a chlorine-based gas and argon gas in an ICP-RIE apparatus to form holes 14H1 and 14H2, which were elongated cylindrical holes dug perpendicular to the GaN surface. In this process, the holes dug in the GaN surface by this etching are hereinafter simply referred to as holes to distinguish them from air holes in the photonic crystal layer 14P. [S3c: Cleaning process] The substrate in which the holes 14H1 and 14H2 are formed is degreased and cleaned, and then the Si x N y The film was removed. Figure 4 shows an SEM (Scanning Electron Microscope) image of the GaN surface at this time.

[0043] As shown in the surface SEM image in Figure 4, a plurality of hole pairs 14H (main holes 14H1 and sub-holes 14H2) were formed in a square lattice pattern, i.e., two-dimensionally on the square lattice points, with a period PC of 164 nm. The holes 14H1 and 14H2 are approximately oval cylindrical holes or apertures that open to the top surface (GaN surface).

[0044] More specifically, the major axis LH1 of the opening of the main hole 14H1 on the GaN surface was 124 nm and the minor axis WH1 was 50 nm (RH1 = major axis / minor axis = 2.49), and the major axis LH2 of the opening of the sub-hole 14H2 was 57.1 nm and the minor axis WH1 was 50.0 nm (RH2 = major axis / minor axis = 1.14).

[0045] In this case, the distances in the x and y directions between the center of gravity CD1 of the main hole 14H1 and the center of gravity CD2 of the sub-hole 14H2 were 65.3 nm (=0.4 × PC), respectively. The major axes of the main hole 14H1 and the sub-hole 14H2 were arranged parallel to the <11-20> axis (i.e., the a-axis).

[0046] 4, the x and y directions are inclined at 45° with respect to the long axis direction (<11-20> direction) and the short axis direction (<1-100> direction) of the opening of the main hole 14H1 and the opening of the sub-hole 14H2, respectively. In this specification, the x and y coordinates are also referred to as hole coordinates. [S3d: Buried layer formation process] This substrate was again introduced into the reactor of the MOVPE apparatus, and ammonia (NH3) was supplied to raise the temperature to 950°C (first embedding temperature). Trimethylgallium (TMG) and NH3 were then supplied to block the opening of the main hole 14H1 and the sub-hole 14H2, thereby forming the first embedded layer 14B1.

[0047] First, during the temperature rise process (temperature rise) to the first temperature range (800°C or higher and 1100°C or lower), Ga atoms on the surface of the growth substrate undergo mass transport in the supplied NH3 atmosphere, forming an overhang consisting of {1-101} and {1-100} planes that closes the opening of the hole formed in the n-cladding layer.

[0048] Next, the TMG supplied after the temperature reaches the first temperature region causes the eaves to grow toward the center of the holes and coalesce, thereby closing and filling the main hole 14H1 and the sub-hole 14H2, thereby forming a first buried layer 14B1.

[0049] Next, after the main hole 14H1 and the sub-hole 14H2 were blocked, a second buried layer 14B2 with a thickness of 50 nm was grown. The second buried layer 14B2 was grown by lowering the substrate temperature to 820°C (second burying temperature) and then supplying triethylgallium (TEG) and trimethylindium (TMI) as a Group 3 atom source and NH3 as a nitrogen source. The second burying temperature was lower than the first burying temperature, at 700°C or higher but lower than 900°C.

[0050] In addition, the In composition of the second buried layer 14B2 in this embodiment is 2% (i.e., Ga 0.98 In 0.02 Second embedded layer 14B2 functions as a light distribution adjusting layer for adjusting the coupling efficiency (light field) between light and photonic crystal layer 14P.

[0051] By the above embedding process, a photonic crystal layer 14P having a double lattice structure in which a pair of holes 14K, each consisting of a main hole 14K1 and a sub-hole 14K2, is arranged at each of the square lattice points is formed. [S4: Light-emitting layer formation process] Next, a multiple quantum well (MQW) layer was grown as the active layer 15, which is the light-emitting layer. The barrier and well layers of the MQW were GaN and InGaN, respectively. The barrier layer was grown by cooling the substrate to 820°C and then supplying triethylgallium (TEG) as a group 3 atom source and NH3 as a nitrogen source. The well layer was grown at the same temperature as the barrier layer, supplying TEG and trimethylindium (TMI) as group 3 atom sources and NH3 as a nitrogen source. The center wavelength of the photoluminescence (PL) from the active layer in this example was 412 nm. [S5: p-guide layer formation process] After the active layer was grown, the substrate temperature was raised to 1050° C., and GaN was grown to a thickness of 120 nm as the p-guide layer 16. The p-guide layer 16 was grown without doping with a dopant, by supplying TMG and NH 3 . [S6: Electron barrier layer formation process] After growing the p-guide layer 16, the electron barrier layer (EBL) 17 was grown while maintaining the substrate temperature at 1050°C. The EBL 17 was grown by supplying TMG and TMA as the group III atom source and NH3 as the nitrogen source. Cp2Mg was also supplied as the p-dopant. This resulted in the formation of an EBL 17 with an Al composition of 18% and a layer thickness of 15 nm. [S7: p-cladding layer formation process] After the growth of the electron barrier layer (EBL) 17, the p-cladding layer 18 was grown while maintaining the substrate temperature at 1050°C. The p-cladding layer 18 was grown by supplying TMG and TMA as the group 3 atom source and NH3 as the nitrogen source. Cp2Mg was also supplied as the p-dopant. As a result, a p-cladding layer 18 with an Al composition of 6% and a layer thickness of 600 nm was formed. After the growth, activation was performed in an N2 atmosphere at 850°C for 10 minutes, and the carrier concentration of the p-cladding layer (p-AlGaN) 18 was 2×10 17 cm -3 It was. [S8: p-contact layer formation process] After growing the p-cladding layer 18, the p-contact layer 19 was grown while maintaining the substrate temperature at 1050° C. The growth of the p-contact layer 19 was carried out by supplying TMG as a group 3 atom source, NH as a nitrogen source, and CpMg as a dopant. [S9: Electrode formation process] The surface of the p-contact layer 19 of the substrate with the epitaxially grown layer is attached to a support substrate, and the substrate 12 is thinned to a predetermined thickness using a polishing device.

[0052] Thereafter, a mask covering the p-contact layer 19 side except for the isolation trench was formed, and etching was performed until the n-clad layer 13 or the substrate 12 was exposed. Thereafter, the mask was removed, the support substrate was removed, and the isolation trench was formed. [S10: Electrode formation process] (Anode electrode formation) A palladium (Pd) film and a gold (Au) film were formed in this order as a p-electrode 20B on the surface of the epitaxial growth substrate 12 by electron beam evaporation. The formed electrode metal film was then photolithographically cut to a size of 200 × 200 μm. 2 The p-electrode 20B was formed by patterning. (Cathode electrode formation) Subsequently, Ti and Au were deposited in this order on the back surface of the substrate 12 by electron beam evaporation to form an n-electrode 20A. [S11: Protective film formation process] After the electrodes were formed, the bottom surface of the substrate was attached to a support substrate, and a mask was formed to cover the anode electrode. After that, a SiO2 protective film was formed on the top and side surfaces of the element by sputtering. [S12: Singulation process] Finally, laser scribing was performed along the center lines of the substrate separation grooves to obtain individualized PCSEL elements (hereinafter referred to as PCSEL elements or simply PCSELs) 10. 2. Main and secondary voids To confirm the shape of the buried voids in this example, the layered structure was processed from the surface using a focused ion beam (FIB) until the voids in the void layer were exposed, and then SEM observation was performed. The void shapes of the main void 14K1 and the subvoid 14K2, which is smaller than the main void 14K1, at this time are shown in the top SEM image of Figure 5. Note that the subvoid 14K2 only needs to be smaller than the main void 14K1 in at least one of the void diameter and depth.

[0053] 6A is an SEM image showing a cross section taken along line AA in FIG. 5, and FIG. 6B is an SEM image showing a cross section taken along line BB in FIG.

[0054] As shown in Figure 5, the major axis LK1 of the primary void 14K1 was 75.2 nm, the minor axis WK1 was 45 nm, and the ratio of the major axis to the minor axis (major axis / minor axis) RK1 = 1.67, and the major axis LK2 of the secondary void 14K2 was 45.8 nm, the minor axis WK2 was 39.2 nm, and the ratio of the major axis to the minor axis (major axis / minor axis) RK2 = 1.17.

[0055] As shown in FIGS. 6A and 6B, the depth DK1 of the main void 14K1 was 102 nm, and the depth DK2 of the subvoid 14K2 was 78.5 nm.

[0056] In this way, it was confirmed that a photonic crystal layer 14P was formed in which hole pairs, each consisting of a primary hole 14K1 and a secondary hole 14K2, were arranged at each square lattice point with a period Pc = 164 nm. That is, the primary hole 14K1 was arranged at the square lattice point with the period Pc, and the secondary hole 14K2 was arranged at the square lattice point with the same period Pc. The hole pairs were arranged so that the distance between the center of gravity D1 of the primary hole 14K1 and the center of gravity D2 of the secondary hole 14K2 (center-to-center distance) was Δx in the x direction and Δy (constant) in the y direction.

[0057] In this specification, the "distance between the centers of gravity" of a main void and a subvoid refers to the distance between the central axis of the main void and the central axis of the subvoid, and is expressed as the distance between the subvoid and the main void in the x and y directions.

[0058] The main voids 14K1 and the subvoids 14K2 had a long hexagonal prism shape with their major axes parallel to the <11-20> axis. The main voids 14K1 and the subvoids 14K2 had {1-102} facets at their bottoms (on the substrate 12 side), but the rest of the voids had a long hexagonal prism shape.

[0059] Specifically, the distances Δx and Δy between the center of gravity D1 of the main void 14K1 and the center of gravity D2 of the subvoid 14K2 were both 65.4 nm (Δx = Δy = 0.4 × PC), and had not changed since before filling. In addition, the major axes of the main void 14K1 and the subvoid 14K2 were arranged so as to be parallel to the <11-20> axis (i.e., the a-axis).

[0060] In this specification, the "long axis or short axis" of a hole (or void) refers to the long axis or short axis of the cross section (opening plane) of the hole in a plane parallel to the photonic crystal layer.

[0061] The percentage of the hole area as viewed from a direction perpendicular to the plane of the photonic crystal layer 14P divided by the square of the hole period PC is called the hole filling factor FF. The hole filling factors FF1 and FF2 of the main hole 14K1 and the subhole 14K2 were calculated to be FF1=10.5% and FF2=5.1%. 3. Device characteristics and evaluation 3.1 Double lattice structure and single lattice structure (1) Comparative Example 1 As Comparative Example 1 for the PCSEL device 10 according to this embodiment, a PCSEL device in which a single void (single-lattice photonic crystal) was formed at a lattice point was fabricated. The only difference from the above manufacturing process is S3b (void formation step), and this point will be explained below.

[0062] 7 is an SEM image showing cylindrical holes CH formed on the GaN surface in Comparative Example 1. Specifically, the holes CH have perfect circular openings with a diameter of 80 nm, and are arranged at square lattice points with a period Pc of 164 nm in the x and y directions.

[0063] More specifically, a resist pattern was formed so that the x-axis, which is the hole arrangement direction, was parallel to the <1-100> axis (i.e., the m-axis) and the y-axis was parallel to the <11-20> axis (i.e., the a-axis). Dry etching was then performed using an ICP-RIE system to form cylindrical holes 14C arranged in a square lattice pattern in the x and y directions. The diameter of the cylindrical holes 14C was 79 nm, and the period PC was 164 nm. (2) Threshold gain (coupled wave theory) The optical confinement coefficients (Γact) of the active layer and the optical confinement coefficients (Γmg) of the Mg-doped layers (p-contact layer, p-cladding layer, and electron barrier layer) were estimated from the electric field intensity distribution of the fundamental mode in the structures of Example 1 and Comparative Example 1. In addition, the cavity loss (α p ), the cavity loss in the direction perpendicular to the photonic crystal layer 14P (α n ) were estimated. These are shown in Table 1.

[0064] In both Example 1 and Comparative Example 1, the absorption coefficient αmg of the Mg-doped layer was 160 cm -1 From Γmg and αmg, the absorption loss αi in each structure that satisfies the following (Equation 1) was calculated as the value shown in Table 1.

[0065] αi = Γmg × αmg (Equation 1) The threshold gain Gth of the laser is calculated by (Equation 2), and as shown in Table 1, in Example 1 it is 1119 cm -1 , and 724 cm in Comparative Example 1 -1 It was estimated that:

[0066] Γact Gth = α p +α n + αi (Equation 2)

[0067] [Table 1]

[0068] In Table 1, α of Example 1 n is α of Comparative Example 1 n This is because the double lattice structure breaks the rotational symmetry of the lattice point structure. In Comparative Example 1, the lattice point structure has two-fold rotational symmetry, so that light diffracted in the vertical direction among the light propagating through the hole layer is canceled out by evanescent interference. In Example 1, the rotational symmetry is reduced, so this evanescent interference is weakened and more light is diffracted in the vertical direction. That is, α n In other words, α n To increase the lattice point structure, it is desirable to make it one-fold rotationally symmetric, and it is sufficient to make the shape or arrangement such that the set of primary vacancies 14K1 and secondary vacancies 14K2 coincide with each other after a 360° rotation. (3) Light output characteristics, emission spectrum 8A shows the IL characteristics (current-light output characteristics) of the PCSEL device 10 of Example 1 and the PCSEL device of Comparative Example 1, and FIG. 8B shows the emission spectra near the threshold current. The measurements were taken using a pulse current drive with a pulse width of 100 ns and a pulse period of 1 kHz.

[0069] The PCSEL device 10 of Example 1 had a threshold current of 1.24 A (threshold current density: 3.9 kA / cm 2 ), and exhibited strong single-peak laser oscillation. On the other hand, the PCSEL device of Comparative Example 1 exhibited strong single-peak laser oscillation at a threshold current of 0.71 A (threshold current density: 2.2 kA / cm2). The reason why Example 1 has a larger threshold current than Comparative Example 1 is because the threshold gain Gth in Table 1 is increased. In Example 1 and Comparative Example 1, the rate of increase in threshold gain Gth and the rate of increase in threshold current are similar, and it is thought that the increase in threshold current is due to increases in cavity loss and absorption loss, and that even when a double lattice structure is introduced as in Example 1, there is no impact on the quality of the active layer.

[0070] On the other hand, the slope efficiency of the PCSEL device 10 of Example 1 was 0.23 W / A, which was significantly higher than 0.10 W / A of Comparative Example 1. This is because, as mentioned above, in Example 1, α n This is because the vertical leakage of light (i.e., the light component that contributes to output) is large, so a large amount of light can be extracted as output. In other words, by making the lattice points in the hole layer into a double lattice structure, a large output can be obtained with a smaller current. 3.2 Arrangement of main and sub-vacancies in double lattice structure [Example]

[0071] (1) Example 2 and Comparative Example 2 In order to evaluate the surface shape after filling with the double lattice structure, photonic crystal layers with two structures were fabricated, and the steps up to S3d were carried out in the same manner as in the above example to fill the holes.

[0072] More specifically, we investigated two structures in which the main voids and sub-voids have the same size and shape, but the major axis directions of the main voids and sub-voids differ by 90°.

[0073] 9A is a top-view SEM image showing main holes 14H1 and sub-holes 14H2 formed in a GaN surface portion in a structure (structure A) in which main holes and sub-holes are formed similarly to Example 1. Specifically, in structure A (Example 2), hole pairs each consisting of an elongated cylindrical main hole 14H1 with a major axis / minor axis ratio of 2.75 (=79.8 nm / 29 nm) and an elongated cylindrical sub-hole 14H2 with a major axis / minor axis ratio of 1.14 (=42.8 nm / 37.6 nm) are formed in a square lattice pattern with a period PC=164 nm.

[0074] 9B is a top-view SEM image showing main holes CH1 and sub-holes CH2 formed in the GaN surface portion in Comparative Example 2. In Comparative Example 2 (structure B), hole pairs each consisting of an elliptical cylindrical main hole CH1 with a major axis / minor axis ratio of 2.76 (=79.4 nm / 28.8 nm) and an elliptical cylindrical sub-hole CH2 with a major axis / minor axis ratio of 1.10 (=41.8 nm / 37.9 nm) are formed in a square lattice pattern with a period PC=164 nm.

[0075] In structure A (FIG. 9A), the major axes of the main hole 14H1 and the sub-hole 14H2 are arranged parallel to the <11-20> axis (i.e., the a-axis), whereas in structure B (FIG. 9B), the major axes of the main hole CH1 and the sub-hole CH2 are arranged perpendicular to the <11-20> axis (i.e., the a-axis).

[0076] That is, Structure A (Example 2) and Structure B (Comparative Example 2) have main holes and sub-holes of approximately the same size and shape, but the long axis direction of the holes in Structure B (Comparative Example 2) is 90° different from the long axis direction of the holes in Structure A (Example 2).

[0077] Therefore, by filling the main holes 14H1 and the sub-holes 14H2 of structure A, a photonic crystal layer 14P is obtained in which the major axes of the main holes 14K1 and the sub-holes 14K2 are arranged parallel to the <11-20> axis (see FIG. 11A).Furthermore, by filling the main holes CH1 and the sub-holes CH2 of structure B, a photonic crystal layer is obtained in which the major axes of the main holes CK1 and the sub-holes CK2 are arranged perpendicular to the <11-20> axis (see FIG. 11B). (2) Surface roughness of the buried layer 10A and 10B are atomic force microscope (AFM) images showing the surface morphology of the buried layer after filling the primary voids and secondary voids for Structure A (Example 2) and Structure B (Comparative Example 2), respectively. Note that the horizontal axis of the AFM image is the m-axis, and the vertical axis is the a-axis.

[0078] As shown in FIG. 10A, when the long axis of each pore was parallel to the a-axis (<11-20> axis) (Structure A: Example 2), a flat surface with a surface roughness (RMS) of 0.594 nm was obtained.

[0079] On the other hand, as shown in Figure 10B, when the long axis of each pore was perpendicular to the a-axis (Structure B: Comparative Example 2), undulations with a height of about 7 nm appeared on the surface, and the surface roughness (RMS 0.836 nm) was larger than that of Structure A (Example).

[0080] If an active layer is grown on a buried layer with such large irregularities on its surface, the In composition will be non-uniform in the uneven areas, degrading the quality of the active layer. This will increase the threshold current, so it is preferable that the long axis of the holes in the photonic crystal layer is parallel to the a-axis.

[0081] 11A and 11B are top views showing the change in hole shape during the formation of the buried layer. The following discusses the difference in surface roughness of the buried layer between when the long axis of the hole is parallel to the a-axis of the crystal orientation and when it is perpendicular to the a-axis, with reference to these figures.

[0082] When holes are embedded in group III nitrides, mass transport occurs, causing the hole shape to change to a shape composed of thermally stable planes, resulting in the formation of a vacancy. In other words, in a +c-plane substrate, the side of the vacancy changes shape to the {1-100} plane (i.e., m-plane). In other words, the shape changes from an oblong cylindrical shape to a long hexagonal prism whose side is composed of m-planes.

[0083] Figure 11A shows a schematic diagram of the shape change of the vacancies when the long axis of the cylindrical holes is parallel to the a-axis (<11-20> axis) (structure A). After deformation, the size of the holes 14H1 and 14H2 shrinks, but the replacement group III nitride atoms are supplied by mass transport from the surrounding crystal (arrows in the figure). The holes then change shape to long hexagonal pillar-shaped holes 14K1 and 14K2 that are inscribed in the original shape of the holes 14H1 and 14H2.

[0084] On the other hand, Figure 11B shows a schematic diagram of the shape change of the voids when the long axis of the long cylindrical holes is perpendicular to the a-axis (structure B). The size of holes CH1 and CH2 shrinks due to mass transport (arrows in the figure). This shape change is larger than that of holes whose long axis is parallel to the a-axis (Figure 11A).

[0085] In a multilattice photonic crystal, the distance between holes is shorter than in a single-lattice photonic crystal, so adjacent holes (i.e., main and subholes) are spaced at a distance approximately equal to the hole size. Therefore, when the shape of a hole changes due to mass transport, the shape changes of adjacent holes interfere with each other. Large irregularities (height differences) are formed on the embedded surface between areas where the shape changes interfere and areas where they do not. Therefore, as shown in Figure 11B, when the long axis of the hole and the a-axis are perpendicular, large shape changes occur, resulting in surface roughness. On the other hand, when the long axis of the hole and the a-axis are parallel, shape changes can be minimized, and a flat surface is expected to be obtained after embedding. (3) Positional relationship between main and sub-holes and resonator loss When the air holes are arranged in a square lattice pattern in the air hole layer (photonic crystal layer), it is preferable that the air holes have the same feedback effect (diffraction efficiency) in the x-axis direction and the y-axis direction in order to prevent direction-dependent uneven distribution of light within the two-dimensional photonic crystal and to stably obtain laser oscillation at a single wavelength.

[0086] That is, it is preferable that the two-dimensional photonic crystal forming the hole layer is symmetrical with respect to axes tilted at 45° from the x-axis and y-axis of the square lattice. When the main hole 14K1 and the subhole 14K2 have a symmetrical structure with respect to axes tilted at 45° from the x-axis and y-axis, it is preferable that the distances Δx and Δy between the centers of gravity of the main hole 14K1 and the subhole 14K2 in the x-axis and y-axis directions are equal (Δx=Δy).

[0087] In the structure of Example 1, the distances (spacing) Δx and Δy between the centers of gravity of main air holes 14K1 and sub-air holes 14K2 that form photonic crystal layer 14P are changed from 0.0PC to 0.5PC (PC is the period of a square lattice) with Δx = Δy. The resonator loss α in the vertical and horizontal directions with respect to photonic crystal layer 14P is n ,α p 12A and 12B, where the horizontal axis indicates the ratio d to the period PC (i.e., d=Δx / PC=Δy / PC).

[0088] FIG. 12C shows the R calculated from the following (Equation 3): n That is, R n is the total cavity loss (α p +α n ) the vertical cavity loss α n is the percentage.

[0089] R n = α n / (α p +α n ) (Formula 3) In a photonic crystal surface-emitting laser, the slope efficiency ηSE is calculated by subtracting αi from the total loss, including the absorption loss αi, as shown in (Equation 4). n (vertical cavity loss) ratio.

[0090]

number

[0091] Therefore, if the absorption loss αi due to the constituent materials can be made zero, ηSE is R n In other words, in order to increase the output efficiency (i.e., ηSE) of a photonic crystal surface-emitting laser and obtain a photonic crystal surface-emitting laser capable of achieving high output, R n It is desirable to increase

[0092] R in a conventional single-lattice photonic crystal surface-emitting laser (Comparative Example 1) n is about 0.18 from Table 1. In the double-lattice photonic crystal surface-emitting laser (Example 1), R n Conventional laser (R n =0.18), the relative position d (=Δx / PC=Δy / PC) of the sub-void to the main void is preferably 0.06 or more or 0.47 or less, as shown in FIG. 12C. (4) Oscillation mode Referring to FIG. 12C, when the distance (spacing) Δx, Δy (Δx=Δy) between the centers of gravity of the main void 14K1 and the sub-void 14K2 is 0.28×PC and 0.40×PC, R n changes discontinuously because the oscillation mode changes at the boundary of the distance between the centers of gravity.

[0093] Figure 13 shows the photonic band structure near the Γ point of a square lattice photonic crystal. In a photonic crystal surface-emitting laser, the standing wave state of light at the band edge of the Γ point of the photonic band structure of the hole layer is used as the resonance effect. At the band edge of the Γ point, there are four band edge modes (shown by black circles) A, B, C, and D, from the lowest frequency side. Of the four band edge modes, laser oscillation is obtained in the mode with the lowest threshold gain (smallest cavity loss).

[0094] In Example 1, the threshold gain (resonator loss) of each mode obtained from the coupled-wave theory when the distances Δx and Δy between the centers of gravity are changed is shown in FIG. 14. It can be seen that for 0.28×PC or less (d≦0.28), mode A; for 0.28PC to 0.40PC (0.28<d<0.40), mode D; and for 0.40PC or more (0.40≦d), mode B becomes the mode with the lowest threshold gain.

[0095] FIG. 15 schematically shows the refractive index, carrier density, and photon density in the current injection region during laser oscillation of a surface-emitting laser. In a group-III nitride semiconductor, generally, due to the carrier plasma effect, the refractive index of the current injection region becomes low. On the other hand, in a semiconductor laser, since the stimulated emission rate is high and the carrier density is low at the center of the resonator where the photon density is high, and also because the temperature of the central part rises due to heat generation, the refractive index of the central part of the current injection region becomes higher than that of its surroundings.

[0096] FIG. 16A schematically shows the frequencies of the photonic band edges at the Γ point in the vicinity of the current injection region during current injection in the case of band-edge modes A and B, and FIG. 16B shows the same in the case of band-edge modes C and D.

[0097] The frequency ω is expressed as (Equation 5) using the refractive index n, the speed of light c, and the wave number k.

[0098] ω = c / n × k (Equation 5) From (Equation 5), when the refractive index distribution changes as shown in FIG. 15 due to current injection (laser oscillation), the frequency profiles of the A, B, C, and D modes, which are the respective band-edge modes, also change along with the refractive index change (from a trapezoidal shape to a trapezoidal shape with a concave center), as shown in FIGS. 16A and 16B.

[0099] As shown in FIG. 16A, in the case of band-edge modes A and B (hereinafter simply referred to as modes A and B), the oscillation mode frequency exists within the photonic band gap at the center of the current injection region. Therefore, the presence of photons at the center of the injection region is suppressed, and photons are generated in the region outside the center of the injection region.

[0100] 17A shows a schematic diagram of the refractive index, carrier density, and photon density in the current injection region when oscillating in band edge modes A and B. The solid lines show the case where the photonic band effect is taken into account, and the dashed lines show the case where the photonic band effect is not taken into account.

[0101] Taking the photonic band effect into consideration, as mentioned above, in modes A and B, photons are distributed over a wider region, and as the injection current increases, the photon density is flattened over the entire current region.

[0102] Correspondingly, the carrier density and refractive index are also uniform throughout the current injection region. Therefore, when oscillating in modes A and B, even when a large current is injected for high-power operation, the photon density distribution is flattened throughout the injection region as the current increases, resulting in a stable beam pattern being emitted.

[0103] 16B, in the case of band-edge modes C and D, the oscillation mode frequency exists within the band gap in the region outside the center of the current injection region, and therefore photons are localized in the center of the injection region.

[0104] 17B shows a schematic diagram of the refractive index, carrier density, and photon density in the current injection region when oscillating in band edge modes C and D. The solid lines show the case where the photonic band effect is taken into account, and the dashed lines show the case where the photonic band effect is not taken into account.

[0105] Considering the photonic band effect, photons are concentrated and localized in the center of the current injection region, which causes the carrier density and refractive index to vary significantly locally in the center of the current injection region, resulting in a non-uniform distribution in the current injection region.

[0106] Therefore, when oscillating in band edge modes C and D, if a large current is injected to operate at high power, the photon density distribution becomes localized and concentrated as the current increases, resulting in an unstable beam pattern. Furthermore, when a large current is injected, the carrier density and refractive index distributions become significantly non-uniform, which makes the oscillating operation prone to multi-mode operation and makes it impossible to obtain stable oscillating operation.

[0107] As explained above, in order to obtain stable oscillation when a high current is injected, it is preferable to oscillate in modes A and B, and it is preferable that the relative position d (=Δx / PC=Δy / PC) of the subvoid 14K2 with respect to the main void 14K1 is 0.06PC to 0.28PC (0.06≦d≦0.28) or 0.40PC to 0.47PC (0.40≦d≦0.47). [Example]

[0108] In Example 3, a PCSEL device 11 was investigated, which has a hole layer (photonic crystal layer) with a dual lattice structure consisting of two regular hexagonal prism-shaped main holes 14K1 and sub-holes 14K2. 1. Fabrication process The fabrication process for the PCSEL device 10 of Example 3 is described in detail below. Differences from the fabrication process of the above-described examples and key points are described. The structure of the PCSEL device 10 and the layer configuration of the semiconductor structure layer 11 were the same as those shown in FIG. 1A. [S3b: Hole and air hole formation process] A clean surface was obtained by cleaning a substrate with a growth layer on which an n-type GaN layer was grown as a preparatory layer for n-guide layer 14. This n-type GaN growth layer is a preparatory layer for forming a layer consisting of lower guide layer 14A and photonic crystal layer 14P.

[0109] The substrate with the growth layer was washed to obtain a clean surface, and then a silicon nitride film (Si x N y) was formed using plasma CVD. An electron beam lithography resist was applied on top of this by spin coating, and the resist was placed in an electron beam (EB) lithography system to pattern a two-dimensional periodic structure.

[0110] This resulted in patterning in which aperture pairs, each consisting of a substantially circular main aperture K1 and a sub-aperture K2 smaller than the main aperture K1, were two-dimensionally arranged on a square lattice point with a period PC=164 nm within the resist plane (see FIG. 3).

[0111] More specifically, the centers of gravity CD1 of the main apertures K1 are arranged at square lattice points at a period PC=164 nm in two mutually orthogonal directions (x and y directions), and the centers of gravity CD2 of the sub-apertures K2 are also arranged at square lattice points at a period PC=164 nm in the x and y directions.

[0112] The main aperture K1 had a major axis of 76 nm and a minor axis of 66 nm (major axis / minor axis = 1.15), and the sub-aperture K2 had a major axis of 59 nm and a minor axis of 51 nm (major axis / minor axis = 1.12). The major axis of each aperture was patterned so as to be parallel to the <11-20> axis (i.e., the a-axis).

[0113] The patterning was performed so that the distance Δx=Δy between the centers of gravity of the main opening K1 and the sub-opening K2 in the x and y directions was 65.6 nm (=0.4×164 nm).

[0114] After developing the patterned resist, Si is x N y The film was selectively dry-etched. As a result, main openings K1 and sub-openings K2 arranged at square lattice points with a period of 164 nm were formed in the Si x N y formed to penetrate the membrane.

[0115] Although the main opening K1 and the sub-opening K2 have an elliptical shape that is slightly deviated from a perfect circle, they may be formed to have a perfect circle shape.

[0116] Next, the resist is removed and the patterned Si x Ny Using the film as a hard mask, holes were formed on the GaN surface. The GaN was dry-etched using a chlorine-based gas in an ICP-RIE apparatus to form multiple pairs of holes 14H (main holes 14H1 and sub-holes 14H2) perpendicular to the GaN surface. [S3c: Cleaning process] The substrate in which the holes 14H1 and 14H2 are formed is degreased and cleaned, and then the Si x N y The film was removed. Figure 18 shows an SEM image of the GaN surface at this time.

[0117] 18, a plurality of hole pairs 14H (main holes 14H1 and sub-holes 14H2) were formed in a square lattice pattern, i.e., two-dimensionally on square lattice points, with a period PC of 164 nm. The holes 14H1 and 14H2 are approximately cylindrical holes that open to the top surface (GaN surface).

[0118] More specifically, the major axis LH1 of the opening of the main hole 14H1 on the GaN surface was 76 nm and the minor axis WH1 was 68 nm, i.e., RH1 (= major axis / minor axis) = 1.12, and the major axis LH2 of the opening of the sub-hole 14H2 was 59 nm and the minor axis WH2 was 53 nm, i.e., RH2 (= major axis / minor axis) = 1.11.

[0119] The distances in the x and y directions between the center of gravity CD1 of the main hole 14H1 and the center of gravity CD2 of the sub-hole 14H2 were 65.3 nm (=0.4 × PC), respectively. The major axes of the main hole 14H1 and the sub-hole 14H2 were arranged parallel to the <11-20> axis (i.e., the a-axis).

[0120] Although the main hole 14H1 and the sub-hole 14H2 have an elongated cylindrical shape that is slightly deviated from a perfect cylindrical shape, they may be formed to have a perfect cylindrical shape. [S3d: Buried layer formation process] This substrate was again introduced into the reactor of the MOVPE apparatus, and ammonia (NH3) was supplied to raise the temperature to 950°C (first embedding temperature). Trimethylgallium (TMG) and NH3 were then supplied to block the opening of the main hole 14H1 and the sub-hole 14H2, thereby forming the first embedded layer 14B1.

[0121] In this temperature range, N atoms are attached to the top surface of the growth substrate, so N-polar faces grow preferentially. Therefore, {1-101} facets grow preferentially on the surface. When the opposing {1-101} facets collide with each other, the holes are blocked and buried in the GaN layer.

[0122] Next, after the main hole 14H1 and the sub-hole 14H2 were blocked, a second buried layer 14B2 having a thickness of 50 nm was grown. The second buried layer 14B2 was grown by lowering the substrate temperature to 820°C (second burying temperature) and then supplying triethylgallium (TEG) and trimethylindium (TMI) as Group 3 atom sources and NH3 as a nitrogen source.

[0123] The In composition of the second buried layer 14B2 is 2% (i.e., Ga 0.98 In 0.02 Second embedded layer 14B2 functions as a light distribution adjusting layer for adjusting the coupling efficiency (light field) between light and photonic crystal layer 14P. [S4: Light-emitting layer formation process] Next, a multiple quantum well (MQW) layer was grown as the active layer 15, which is the light-emitting layer. More specifically, as in the above-mentioned examples, the barrier and well layers of the MQW were GaN and InGaN, respectively. The barrier layer was grown by cooling the substrate to 820°C and then supplying triethylgallium (TEG) as a group 3 atom source and NH3 as a nitrogen source. The well layer was grown at the same temperature as the barrier layer, by supplying TEG and trimethylindium (TMI) as group 3 atom sources and NH3 as a nitrogen source. The center wavelength of PL emission from the active layer in this example was 412 nm.

[0124] The steps from S5 (p-side guide layer formation step) onwards were the same as the fabrication steps described above, and the PCSEL device 10 of Example 3 was formed. 2. Main and secondary voids To confirm the shape of the embedded air holes formed in the examples, the layered structure was processed from the surface using FIB until the pores in the pore layer were exposed, and then SEM observation was performed. The pore shapes of the main pore 14K1 and the subpore 14K2, which is smaller than the main pore 14K1, are shown in the top SEM image of Figure 19A. Note that the subpore 14K2 only needs to be smaller than the main pore 14K1 in at least one of the pore diameter and depth.

[0125] 19B is an SEM image showing a cross section taken along line AA in FIG. 19A, and FIG. 19C is an SEM image showing a cross section taken along line BB in FIG. 19A.

[0126] 19A, it was confirmed that the primary voids 14K1 and the subvoids 14K2 had a hexagonal shape. Furthermore, SEM observation revealed that the major axis LK1 of the primary void 14K1 was 57.2 nm, the minor axis WK1 was 49.5 nm, and the ratio of the major axis to the minor axis (major axis / minor axis) RK1 was 1.15. Furthermore, the depth DK1 of the primary void 14K1 was 91.3 nm.

[0127] The major axis LK2 of the subvoid 14K2 was 43.5 nm, the minor axis WK2 was 37.7 nm, and the ratio of the major axis to the minor axis (major axis / minor axis) RK2 was 1.15. The depth DK2 of the subvoid 14K2 was 79.4 nm.

[0128] The ratio of the major axis to the minor axis of a regular hexagon is RR=2 / 3 1 / 2 =1.15, it was confirmed from the ratio RK1 of the main void 14K1 and the ratio RK2 of the subvoid 14K2 that the main void 14K1 and the subvoid 14K2 have a regular hexagonal prism shape.

[0129] Furthermore, the distances (distances between centers of gravity) Δx and Δy between the center of gravity D1 of the main void 14K1 and the center of gravity D2 of the subvoid 14K2 were 65.4 nm (=0.4×PC), respectively, and were unchanged from before the filling.

[0130] The major axes of the main voids 14K1 and the sub-voids 14K2 were arranged so as to be parallel to the <11-20> axis (that is, the a-axis). 3. Device characteristics and evaluation (1) Comparative Examples 1 and 2 In evaluating the PCSEL device 10 according to Example 3, it was compared with the PCSEL device of Comparative Example 1, which has a single lattice structure in which a single void is formed at a lattice point. It was also compared with the PCSEL device of Comparative Example 2, in which the major axis directions of the main voids and sub-voids differ by 90° from those of Example 3. (2) Threshold gain (coupled wave theory) The optical confinement coefficients (Γact) of the active layer and the optical confinement coefficients (Γmg) of the Mg-doped layers (p-contact layer, p-cladding layer, and electron barrier layer) were estimated from the electric field intensity distribution of the fundamental mode in the structures of Example 3 and Comparative Example 1. In addition, the cavity loss (α p ), the cavity loss in the direction perpendicular to the photonic crystal layer 14P (α n ) was estimated.

[0131] In both Example 3 and Comparative Example 1, the absorption coefficient α of the Mg-doped layer mg is 160cm -1 The optical confinement factor (Γmg) and absorption coefficient α mg From the above (Equation 1), the absorption loss α i The threshold gain Gth of the laser was calculated by the above formula (2), and as shown in Table 2, in Example 3 it was 1068 cm -1 , and 724 cm in Comparative Example 1 -1 These are summarized in Table 2.

[0132] [Table 2]

[0133] In Table 2, α of Example 3 n is α of Comparative Example 1 nThis is because the double lattice structure breaks the 90° rotational symmetry of the lattice point structure. In Comparative Example 1, since the lattice point structure has 90° rotational symmetry, light diffracted in the vertical direction among light propagating through the hole layer is canceled out by evanescent interference.

[0134] In Example 3, the 90° rotational symmetry is reduced, so this evanescent interference is weakened and more light is diffracted in the vertical direction. n is increasing.

[0135] Thus, it was confirmed that in Example 3, in which the main holes 14K1 and the sub-holes 14K2 have a regular hexagonal prism shape, the light component propagating in the vertical direction is significantly increased compared to a photonic crystal layer with a single lattice structure. (3) Light output characteristics, emission spectrum The IL characteristics (current-light output characteristics) of the PCSEL device 10 of Example 3 and the PCSEL device of Comparative Example 1 are shown in Figure 20A, and the emission spectra near the threshold current are shown in Figure 20B. The measurements were taken using pulse current drive with a pulse width of 100 ns and a pulse period of 1 kHz.

[0136] The PCSEL device 10 of Example 3 had a threshold current of 1.21 A (threshold current density: 3.8 kA / cm 2 ), and laser oscillation with a strong single peak was observed. On the other hand, the PCSEL device of Comparative Example 1 exhibited laser oscillation with a strong single peak at a threshold current of 0.71 A (threshold current density: 2.2 kA / cm2). The reason why the threshold current of Example 3 is larger than that of Comparative Example 1 is because the threshold gain Gth shown in Table 2 is increased.

[0137] In Example 3 and Comparative Example 1, the rate of increase in threshold gain Gth and the rate of increase in threshold current are similar, and it is considered that the increase in threshold current is due to an increase in cavity loss and absorption loss. Therefore, even when a double lattice structure is introduced as in Example 3, it is considered that there is no effect on the quality of the active layer.

[0138] On the other hand, the slope efficiency of the PCSEL device 10 of Example 3 was 0.35 W / A, which was significantly higher than 0.10 W / A of Comparative Example 1. This is because, as mentioned above, in Example 3, α n This is because the vertical propagation of light is large (i.e., the increase in the vertical propagation of light) and therefore the amount of light extracted as output is large. In other words, by using a double lattice structure in the hole layer, it is possible to obtain a large output with a smaller current. (4) Positional relationship between main and sub-holes and resonator loss In Example 3, a PCSEL device was fabricated having a hole layer with a double lattice structure consisting of two lattice points, regular hexagonal prism-shaped main holes 14K1 and sub-holes 14K2.

[0139] In the structure of Example 3, the cavity loss α in the vertical and horizontal directions with respect to the photonic crystal layer 14P when the distances Δx, Δy (Δx=Δy) between the centers of gravity of the main air holes 14K1 and the sub-air holes 14K2 are changed in the range of 0.0PC to 0.5PC (PC is the period of the square lattice) is n ,α p 21A and 21B, where the horizontal axis represents the ratio d of the center-of-gravity distances Δx and Δy (the spacing between the main and sub-holes) to the square lattice period PC (i.e., d=Δx / PC=Δy / PC).

[0140] FIG. 21C shows the R calculated from the above (Equation 3). n This shows the dependence of the distance between the centers of gravity on R n is the total cavity loss (α p +α n ) the vertical cavity loss α n is the percentage.

[0141] In addition, in a photonic crystal surface-emitting laser, the slope efficiency η SE is calculated by the ratio α n (vertical cavity loss) ratio.

[0142] Therefore, if the absorption loss αi due to the constituent materials can be made zero, ηSE is nIn other words, in order to increase the output efficiency (i.e., ηSE) of a PCSEL device and obtain a PCSEL device that can achieve high output, R n It is desirable to increase

[0143] R in a conventional PCSEL device with a single grating structure (Comparative Example 1) n is about 0.18 from Table 2. In the PCSEL device of Example 3 having a double lattice structure consisting of main voids and sub-voids in the shape of regular hexagonal pillars, R n The PCSEL element (R n =0.18), the distance between the centers of gravity (relative position d) of the main void 14K1 and the sub-void 14K2 (=Δx / PC=Δy / PC) is preferably 0.06 or more or 0.47 or less, as shown in FIG. 21C.

[0144] It is thought that it is possible to break the four-fold (90°) rotational symmetry of the spatial refractive index distribution within the lattice point by making the air hole shape a long hexagonal prism with a larger long axis / short axis ratio. However, even with a regular hexagonal prism-shaped air hole with a small long axis / short axis ratio of 1.15, a high R n It was found that it is possible to obtain

[0145] However, in PCSEL devices using GaN-based materials, it is preferable to change the shape of the pore sidewalls to thermally stable m-planes during growth in order to stably fill the pores. In other words, it is preferable that the ratio of the major axis to the minor axis of the pores forming the pore layer is at least 1.15. (5) Oscillation mode FIG. 21D shows the threshold gain (resonator loss) of each mode obtained from the coupled-wave theory when the relative position d (=Δx / PC=Δy / PC) of the subhole 14K2 with respect to the main hole 14K1 is changed in Example 3.

[0146] When the relative position d is 0.24×PC or less (d≦0.24), it is mode A; when it is 0.24PC to 0.28PC (0.24 < d≦0.28), it is mode B; when it is 0.28PC to 0.34PC (0.28 < d < 0.34), it is mode C; when it is 0.34PC to 0.40PC (0.34≦d < 0.40), it is mode D; when it is 0.40PC or more (0.40≦d), it can be seen that mode B becomes the mode with the smallest threshold gain.

[0147] As described with reference to FIGS. 16A and 16B, in order to obtain stable oscillation when a high current is injected, it is preferable to oscillate in modes A and B. (6) Hole filling factor (FF: filling factor) In the structure of Example 3, with the hole filling factor FF2 of the auxiliary hole 14K2 fixed at 4.5%, the resonator loss when the hole filling factor FF1 of the main hole 14K1 was varied from 4.5% to 40% was determined by two-dimensional coupled wave theory. R with respect to the hole filling factor ratio FF1 / FF2 n , the sum of the resonator losses in the vertical and horizontal directions (α n +α p ) are shown in FIGS. 22A and 22B, respectively.

[0148] As described above, in this specification, the hole filling factor is the ratio of the area occupied by each hole per unit area of a two-dimensional periodic array. Specifically, assuming that the areas of the main hole 14K1 and the auxiliary hole 14K2 in the hole layer are S1 and S2, respectively, in the case of a square lattice (period PC), the hole filling factor FF1 of the main hole 14K1 = S1 / PC 2 , and the hole filling factor FF2 of the auxiliary hole 14K = S2 / PC 2 .

[0149] Generally, the photonic band structure near the Γ point of a square lattice photonic crystal is as shown in FIG. 13 described above, and there are 4 band-edge modes. As shown in FIGS. 22A and 22B, as the hole filling factor ratio FF1 / FF2 changes, the band-edge mode with the smallest loss also changes.

[0150] [[ID=!]] As explained in detail in Examples 1 and 2, in order to obtain stable oscillation when a high current is injected, it is preferable to oscillate in Modes A and B. That is, to oscillate in Modes A and B, it is preferable that the hole filling factor ratio RF=FF1 / FF2 is in the range of 1.7 to 7.5, that is, 1.7≦(FF1 / FF2)≦7.5, as shown in Figures 22A and 22B.

[0151] In the above-described embodiments, the primary voids 14K1 and the secondary voids 14K2 have a long hexagonal prism shape and a regular hexagonal prism shape, but the secondary voids 14K2 may have a cylindrical shape with a perfectly circular cross section, a regular hexagonal prism shape, or the like.

[0152] Although the cases where the main holes 14K1 after embedding have a long hexagonal prism shape and a regular hexagonal prism shape have been described, the present invention is not limited thereto. The main holes 14K1 may have an elongated cylindrical shape, or may have an intermediate shape in the process in which the holes change from a cylindrical shape or an elongated cylindrical shape to a regular hexagonal prism shape or a long hexagonal prism shape due to embedding growth. Therefore, in this specification, the term "regular hexagonal prism shape, elongated hexagonal prism shape, or elongated cylindrical shape" includes intermediate shapes in the process in which the holes change from a cylindrical shape or an elongated cylindrical shape to a regular hexagonal prism shape or a long hexagonal prism shape.

[0153] Furthermore, when the primary void 14K1 has a regular hexagonal prism shape, a long hexagonal prism shape, or an oblong cylinder shape whose major axis is parallel to the <11-20> axis, the secondary void 14K2 may have a regular hexagonal prism shape, a long hexagonal prism shape, or an oblong cylinder shape whose major axis is parallel to the <11-20> axis.

[0154] Furthermore, in the above-described embodiment, the photonic crystal layer 14P is described in which a hole pair consisting of a main hole 14K1 and a sub-hole 14K2 is arranged at each square lattice point. However, a multi-lattice photonic crystal layer may be configured in which a hole set consisting of a main hole 14K1, a sub-hole 14K2, and at least one hole is arranged at each square lattice point.

[0155] The numerical values ​​in the above-described embodiment are merely examples and can be appropriately modified and applied.

[0156] As described above in detail, according to the above-described embodiment, it is possible to provide a photonic crystal surface-emitting laser (PCSEL) element in which the flatness of the surface of the burying layer in which the multi-lattice photonic crystal is buried is greatly improved, and a method for manufacturing the same.

[0157] Furthermore, it is possible to provide a photonic crystal surface-emitting laser having an active layer grown on a multi-lattice photonic crystal layer with high quality and crystallinity, high light extraction efficiency, and capable of oscillating at a low threshold current density and high quantum efficiency, and a method for manufacturing the same. [Explanation of symbols]

[0158] 10: PCSEL element, 11: semiconductor structure layer, 12: substrate, 13: first cladding layer, 14: first guide layer, 14A: lower guide layer, 14P: photonic crystal layer (PC layer), 14B: buried layer, 15: active layer, 16: second guide layer, 17: electron barrier layer, 18: second cladding layer, 19: contact layer, 20A: first electrode, 20B: second electrode, 20L: light emission region, 25: second buried layer, CD1, CD2: center of gravity, K1 / K2: main / secondary aperture, 14H1 / 14H2: main / secondary hole, 14K1 / 14K2: main / secondary hole

Claims

1. A method for manufacturing a surface-emitting laser element, comprising: forming a guiding layer on a growth substrate; forming an etching mask on the guide layer, the etching mask having an opening set including at least a main opening and a sub-opening having a size smaller than that of the main opening at each square lattice point; etching the guide layer using the etching mask to form main holes and sub-holes; performing crystal growth including mass transport to form a buried layer that closes the openings of the main holes and sub-holes, thereby forming a multi-lattice photonic crystal layer in which a hole set including a main hole and a sub-hole having a hole diameter and depth smaller than those of the main hole is arranged at each of the square lattice points; forming a semiconductor layer including an active layer on the multi-lattice photonic crystal layer, the semiconductor constituting the buried layer has anisotropy due to a crystal plane in the shape change rate caused by the burying of the mass transport; The method for manufacturing a surface-emitting laser element, wherein the main hole is etched into a long hexagonal prism or an oval cylindrical shape with the direction in which the shape change rate is slow as a minor axis direction.

2. A method for manufacturing a surface-emitting laser element, comprising: forming a guiding layer on a growth substrate; forming an etching mask on the guide layer, the etching mask having an opening set including at least a main opening and a sub-opening having a size smaller than that of the main opening at each square lattice point; etching the guide layer using the etching mask to form main holes and sub-holes; performing crystal growth including mass transport to form a buried layer that closes the openings of the main holes and sub-holes, thereby forming a multi-lattice photonic crystal layer in which a hole set including a main hole and a sub-hole having a hole diameter and depth smaller than those of the main hole is arranged at each of the square lattice points; forming a semiconductor layer including an active layer on the multi-lattice photonic crystal layer, the main cavity formed from the main hole has a regular hexagonal prism shape or a long hexagonal prism shape with a major axis parallel to a <11-20> axis, and the side surface of the main cavity has a {1-100} plane.

3. 3. The method for manufacturing a surface-emitting laser element according to claim 1, wherein the sub-holes have a regular hexagonal prism shape, a long hexagonal prism shape, or an oval cylindrical shape with their major axes parallel to the <11-20> axis.

4. A surface-emitting laser element made of a group III nitride semiconductor, a first guide layer including: a photonic crystal layer formed on a c-plane of a substrate which is a group III nitride semiconductor, the photonic crystal layer having holes arranged in a hole-forming region with two-dimensional periodicity in a plane parallel to the layer; and a buried layer formed on the photonic crystal layer and closing the holes; an active layer formed on the first guide layer; a second guide layer formed on the active layer, a hole set including at least a main hole and a sub-hole having a hole diameter and a hole depth smaller than those of the main hole is arranged at each of the square lattice points in a plane parallel to the photonic crystal layer, the hole formation region is a partial region of the photonic crystal layer, The main holes have a regular hexagonal prism shape, an elongated hexagonal prism shape, or an elongated cylindrical shape with the major axis parallel to the <11-20> axis.

5. a first annular electrode provided on a rear surface of the substrate and electrically connected to the substrate; the hole formation region is a region that is included in the first electrode when viewed from a direction perpendicular to the photonic crystal layer; 5. The surface-emitting laser element according to claim 4.

6. 6. The surface-emitting laser element according to claim 4, wherein the hole formation region has a rectangular shape.

7. a second electrode provided on the second guide layer and electrically connected to the second guide layer; the second electrode is formed in a region included in the hole formation region; 7. The surface-emitting laser element according to claim 4.

8. 8. The surface-emitting laser element according to claim 4, wherein the first guide layer includes an n-type semiconductor layer, and the second guide layer includes a p-type semiconductor layer formed on the n-type semiconductor layer.

9. 9. The surface-emitting laser device according to claim 4, wherein the hole set includes the main hole, the sub-hole, and at least one other hole.

10. 10. The surface-emitting laser element according to claim 4, wherein the photonic crystal layer is made of GaN, and the buried layer includes a layer containing In (indium) in its composition.

11. 11. The surface-emitting laser element according to claim 4, wherein the sub-hole has a regular hexagonal prism shape, an elongated hexagonal prism shape, or an elongated cylindrical shape with a major axis parallel to the <11-20> axis.

12. 12. The surface-emitting laser element according to claim 4, wherein the main hole and the sub-hole have a regular hexagonal prism shape with a major axis parallel to the <11-20> axis.

13. the sets of vacancies are arranged in x and y directions that are orthogonal to each other and at angles of 45° relative to the <11-20> and <1-100> axes; 13. The surface-emitting laser element according to claim 4, wherein relative positions Δx and Δy of the sub-holes with respect to the main hole satisfy Δx = Δy, and when a period of the square lattice points is PC and Δx = Δy = d × PC, 0.06≦d≦0.28 or 0.40≦d≦0.47 is satisfied.

14. 14. The surface-emitting laser element according to claim 4, wherein the main hole and the sub-hole have a hexagonal prism shape with m-plane side faces.

15. 15. The surface-emitting laser element according to claim 4, wherein when the hole filling factors of the main holes and the subholes in the photonic crystal layer are FF1 and FF2, respectively, a hole filling factor ratio RF=FF1 / FF2 satisfies 1.7≦RF≦7.5.

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