JP2014034481A - Sapphire substrate for growing gallium nitride crystal, manufacturing method of gallium nitride crystal, and gallium nitride crystal - Google Patents
Sapphire substrate for growing gallium nitride crystal, manufacturing method of gallium nitride crystal, and gallium nitride crystal Download PDFInfo
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- 239000013078 crystal Substances 0.000 title claims abstract description 73
- 229910002601 GaN Inorganic materials 0.000 title claims abstract description 70
- JMASRVWKEDWRBT-UHFFFAOYSA-N Gallium nitride Chemical compound [Ga]#N JMASRVWKEDWRBT-UHFFFAOYSA-N 0.000 title claims abstract description 70
- 229910052594 sapphire Inorganic materials 0.000 title claims abstract description 46
- 239000010980 sapphire Substances 0.000 title claims abstract description 46
- 239000000758 substrate Substances 0.000 title claims abstract description 46
- 238000004519 manufacturing process Methods 0.000 title claims abstract description 8
- 238000000034 method Methods 0.000 description 9
- 229920002120 photoresistant polymer Polymers 0.000 description 6
- 238000005530 etching Methods 0.000 description 4
- 239000000463 material Substances 0.000 description 3
- 239000003960 organic solvent Substances 0.000 description 3
- 230000000694 effects Effects 0.000 description 2
- GYHNNYVSQQEPJS-UHFFFAOYSA-N Gallium Chemical compound [Ga] GYHNNYVSQQEPJS-UHFFFAOYSA-N 0.000 description 1
- 230000002411 adverse Effects 0.000 description 1
- 230000015572 biosynthetic process Effects 0.000 description 1
- 238000004140 cleaning Methods 0.000 description 1
- 230000008034 disappearance Effects 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 229910052733 gallium Inorganic materials 0.000 description 1
- 238000010438 heat treatment Methods 0.000 description 1
- 229920003986 novolac Polymers 0.000 description 1
- 238000001020 plasma etching Methods 0.000 description 1
- 239000002994 raw material Substances 0.000 description 1
- 229920005989 resin Polymers 0.000 description 1
- 239000011347 resin Substances 0.000 description 1
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L33/00—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
- H01L33/02—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof characterised by the semiconductor bodies
- H01L33/16—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof characterised by the semiconductor bodies with a particular crystal structure or orientation, e.g. polycrystalline, amorphous or porous
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- H—ELECTRICITY
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- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L33/00—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
- H01L33/005—Processes
- H01L33/0062—Processes for devices with an active region comprising only III-V compounds
- H01L33/0066—Processes for devices with an active region comprising only III-V compounds with a substrate not being a III-V compound
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L33/00—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
- H01L33/005—Processes
- H01L33/0062—Processes for devices with an active region comprising only III-V compounds
- H01L33/0075—Processes for devices with an active region comprising only III-V compounds comprising nitride compounds
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01L—SEMICONDUCTOR DEVICES NOT COVERED BY CLASS H10
- H01L33/00—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof
- H01L33/02—Semiconductor devices having potential barriers specially adapted for light emission; Processes or apparatus specially adapted for the manufacture or treatment thereof or of parts thereof; Details thereof characterised by the semiconductor bodies
- H01L33/26—Materials of the light emitting region
- H01L33/30—Materials of the light emitting region containing only elements of Group III and Group V of the Periodic Table
- H01L33/32—Materials of the light emitting region containing only elements of Group III and Group V of the Periodic Table containing nitrogen
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- Microelectronics & Electronic Packaging (AREA)
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Abstract
Description
本発明は、窒化ガリウム結晶成長用サファイア基板、窒化ガリウム結晶の製造方法、及び窒化ガリウム結晶に関するものである。 The present invention relates to a sapphire substrate for gallium nitride crystal growth, a method for producing a gallium nitride crystal, and a gallium nitride crystal.
窒化ガリウム系発光ダイオード(LED)の光取出効率を向上させるための手段として、サファイア基板のC面上に、円錐状若しくは多角形錐状の微小凸部又は微小凹部等の凹凸部を形成し、その上に窒化ガリウム結晶を平坦になるまで成長させ、更にその上に発光層を形成するという手法が用いられる(例えば、特許文献1又は2)。 As a means for improving the light extraction efficiency of a gallium nitride light-emitting diode (LED), on the C surface of the sapphire substrate, a concave or convex portion such as a conical or polygonal pyramid minute convex portion or a minute concave portion is formed, A method is used in which a gallium nitride crystal is grown to a flat surface thereon, and a light emitting layer is further formed thereon (for example, Patent Document 1 or 2).
これらの手法は、表面に凹凸部が形成されたサファイア基板上に窒化ガリウム結晶を成長させると、成長初期の島状成長が促進され、転位同士が会合、消滅することで、平坦な表面のサファイア基板上に窒化ガリウム結晶を成長させた場合に比べて転位の少ない窒化ガリウム結晶が得られるという効果もあり、窒化ガリウム結晶の高品質化にも有効である。 In these methods, when a gallium nitride crystal is grown on a sapphire substrate with a concavo-convex portion formed on the surface, island-like growth at the initial stage of growth is promoted, dislocations associate and disappear, and sapphire has a flat surface. Compared with the case where a gallium nitride crystal is grown on a substrate, there is an effect that a gallium nitride crystal with few dislocations can be obtained, which is effective in improving the quality of the gallium nitride crystal.
近年では、窒化ガリウム結晶のより一層の高品質化が求められており、前述した手法の改良が望まれている。 In recent years, higher quality of gallium nitride crystals has been demanded, and improvement of the above-described method is desired.
そこで、本発明の目的は、従来に比べて窒化ガリウム結晶の更なる低転位化を実現し、窒化ガリウム結晶のより一層の高品質化を可能とする窒化ガリウム結晶成長用サファイア基板、窒化ガリウム結晶の製造方法、及び窒化ガリウム結晶を提供することにある。 Accordingly, an object of the present invention is to realize a further reduction in dislocations in a gallium nitride crystal as compared with the prior art, and to further improve the quality of the gallium nitride crystal. And to provide a gallium nitride crystal.
この目的を達成するために創案された本発明は、サファイア基板のC面上に複数の微小凸部を形成した窒化ガリウム結晶成長用サファイア基板において、前記サファイア基板のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域が前記微小凸部の表面積の5%以上の割合を占める窒化ガリウム結晶成長用サファイア基板である。 In order to achieve this object, the present invention provides a sapphire substrate for gallium nitride crystal growth in which a plurality of minute protrusions are formed on the C-plane of the sapphire substrate, and the a-axis direction of the sapphire substrate is oriented from the C-plane. This is a sapphire substrate for gallium nitride crystal growth in which an area within ± 10 degrees from a plane having an angle of 43.2 degrees accounts for 5% or more of the surface area of the micro-projections.
また、本発明は、前記窒化ガリウム結晶成長用サファイア基板上に窒化ガリウム結晶を成長させる窒化ガリウム結晶の製造方法である。 The present invention is also a method for producing a gallium nitride crystal, wherein a gallium nitride crystal is grown on the sapphire substrate for gallium nitride crystal growth.
また、本発明は、前記製造方法により製造されたことを特徴とする窒化ガリウム結晶である。 In addition, the present invention is a gallium nitride crystal manufactured by the above manufacturing method.
本発明によれば、従来に比べて窒化ガリウム結晶の更なる低転位化を実現し、窒化ガリウム結晶のより一層の高品質化を可能とする窒化ガリウム結晶成長用サファイア基板、窒化ガリウム結晶の製造方法、及び窒化ガリウム結晶を提供することができる。 According to the present invention, a sapphire substrate for growing a gallium nitride crystal, which realizes further lower dislocations of the gallium nitride crystal than in the prior art and enables higher quality of the gallium nitride crystal, manufacture of the gallium nitride crystal Methods and gallium nitride crystals can be provided.
以下、本発明の好適な実施の形態を添付図面にしたがって説明する。 Preferred embodiments of the present invention will be described below with reference to the accompanying drawings.
図1に示すように、本実施の形態に係る窒化ガリウム結晶成長用サファイア基板10は、サファイア基板11のC面(その微傾斜面も含む)上に複数の微小凸部12を形成したものであり、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積の5%以上の割合を占めることを特徴とする。 As shown in FIG. 1, a sapphire substrate 10 for gallium nitride crystal growth according to the present embodiment has a plurality of minute convex portions 12 formed on a C-plane (including a slightly inclined surface) of a sapphire substrate 11. And the region 13 within ± 10 degrees from the surface of the sapphire substrate 11 facing the a-axis direction and having an angle of 43.2 degrees from the C-plane as a reference plane has a ratio of 5% or more of the surface area of the micro-projections 12 It is characterized by occupying.
サファイア基板11のa軸方向を向きC面からの角度が43.2度の面は、その上に窒化ガリウム結晶を成長させた場合に、窒化ガリウム結晶のR面(10−12面)となる面である。その理由を以下に述べる。 The plane of the sapphire substrate 11 facing the a-axis direction and having an angle of 43.2 degrees from the C plane becomes the R plane (10-12 plane) of the gallium nitride crystal when the gallium nitride crystal is grown thereon. Surface. The reason is described below.
異種材料が接合される際には、接合を形成するために必要なエネルギが最小となるように、また異種材料間の格子ひずみを緩和するように、それぞれの材料が接合面内で結晶軸の方位をずらした形で接合される。そのため、サファイア基板11上に窒化ガリウム結晶を成長させる場合には、図2に示すように、窒化ガリウム結晶14がサファイア基板11との接合面でサファイア基板11の結晶軸に対して30度回転して成長される。 When dissimilar materials are bonded, each material has a crystal axis within the bonding plane so that the energy required to form the bond is minimized and the lattice strain between dissimilar materials is reduced. They are joined with their orientations shifted. Therefore, when a gallium nitride crystal is grown on the sapphire substrate 11, the gallium nitride crystal 14 rotates 30 degrees with respect to the crystal axis of the sapphire substrate 11 at the joint surface with the sapphire substrate 11 as shown in FIG. Will grow.
よって、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面は、窒化ガリウム結晶14を成長させる際に回転し、結局、窒化ガリウム結晶14のm軸方向を向きC面からの角度が43.2度の面、即ち窒化ガリウム結晶14のR面となるのである。 Therefore, the plane of the sapphire substrate 11 facing the a-axis direction and the angle of 43.2 degrees from the C plane rotates when growing the gallium nitride crystal 14, and eventually faces the m-axis direction of the gallium nitride crystal 14. This is a plane whose angle from the plane is 43.2 degrees, that is, the R plane of the gallium nitride crystal 14.
窒化ガリウム結晶14のR面は、数ある結晶面の中でも安定しており、窒化ガリウム結晶14の成長時における原料の取込効率が低い面である。そのため、微小凸部12の傾斜面上にある程度の面積でR面に近い領域13が存在すると、R面上での成長が他の面上よりも遅いため、窒化ガリウム結晶成長用サファイア基板10上に窒化ガリウム結晶14のR面で囲まれた六角錐状の構造が形成される。 The R plane of the gallium nitride crystal 14 is stable among a number of crystal planes, and is a surface with low raw material uptake efficiency during the growth of the gallium nitride crystal 14. Therefore, if there is a region 13 close to the R plane with a certain area on the inclined surface of the minute convex portion 12, the growth on the R plane is slower than on the other planes. Thus, a hexagonal pyramid structure surrounded by the R plane of the gallium nitride crystal 14 is formed.
この六角錐状の構造は、R面で囲まれているため、R面以外の面からなる凹凸が形成される場合に比べて安定であり、六角錐状の構造が窒化ガリウム結晶14の成長時に長時間維持され、従来に比べて島状成長が長く続くこととなる。そうすると、転位同士の会合、消滅が従来に比べてより促進され、得られる窒化ガリウム結晶14の更なる低転位化が実現される。 Since this hexagonal pyramidal structure is surrounded by the R plane, the hexagonal pyramidal structure is more stable than the case where irregularities formed from surfaces other than the R plane are formed. It is maintained for a long time, and the island growth lasts longer than before. Then, the association and disappearance of dislocations are further promoted as compared with the conventional case, and further reduction of dislocations in the obtained gallium nitride crystal 14 is realized.
このようなR面からなる六角錐状の構造を得るためには、先に述べたように、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積の5%以上の割合を占める必要があるのである。 In order to obtain such a hexagonal pyramid structure composed of the R plane, as described above, the a-axis direction of the sapphire substrate 11 is oriented, and a plane whose angle from the C plane is 43.2 degrees is used as a reference plane. Therefore, the region 13 within ± 10 degrees needs to occupy a ratio of 5% or more of the surface area of the minute convex portion 12.
なお、表面形状をAFM(原子間力顕微鏡)で測定すれば、表面の微小部分の面積と基準面に対する角度を求めることができる。このAFMを用いて、領域13の基準を満たす部分の面積の合計と、微小凸部12との面積とをそれぞれ求めて、面積割合を算出した。 If the surface shape is measured with an AFM (atomic force microscope), the area of the minute portion of the surface and the angle with respect to the reference plane can be obtained. Using this AFM, the total area of the portions satisfying the criteria of the region 13 and the area of the minute convex portion 12 were obtained, and the area ratio was calculated.
ここで、微小凸部12を形成する方法と、その傾斜面の角度を調整する方法とについて述べる。 Here, a method for forming the minute convex portion 12 and a method for adjusting the angle of the inclined surface will be described.
図3に示すように、先ずサファイア基板11のC面上にレジスト15を塗布する(図3(a))。その後、レジスト15中の余分な有機溶剤を蒸発させるため、レジスト15が塗布されたサファイア基板11をホットプレート上に載置し、数分間の予備加熱を行う。このときの温度はレジスト15の種類によって異なるが、ノボラック系樹脂を用いた場合には120℃程度である。 As shown in FIG. 3, first, a resist 15 is applied on the C surface of the sapphire substrate 11 (FIG. 3A). Thereafter, in order to evaporate excess organic solvent in the resist 15, the sapphire substrate 11 coated with the resist 15 is placed on a hot plate and preheated for several minutes. The temperature at this time varies depending on the type of the resist 15, but is about 120 ° C. when a novolac resin is used.
そして、パターンの露光、現像、及び洗浄等を行い、フォトレジストパターン16を形成する(図3(b))。このとき、六角形パターンのフォトレジストパターン16を形成することで、この後の工程で図1に示したような丸みを帯びた六角錐状の微小凸部12を形成することができ、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積に占める割合を好適に制御することが可能となる。 Then, pattern exposure, development, cleaning, and the like are performed to form a photoresist pattern 16 (FIG. 3B). At this time, by forming the photoresist pattern 16 having a hexagonal pattern, it is possible to form the rounded hexagonal pyramid-shaped minute convex portion 12 as shown in FIG. It is possible to favorably control the ratio of the area 13 within ± 10 degrees to the surface area of the micro-projections 12 with the surface having an angle of 43.2 degrees from the C plane as the reference plane. It becomes.
次いで、予備加熱の温度よりも低い100℃程度に温度制御された紫外線照射装置により、サファイア基板11上のフォトレジストパターン16に紫外線を照射し、レジスト樹脂を架橋、硬化させる。 Next, the photoresist pattern 16 on the sapphire substrate 11 is irradiated with ultraviolet rays by an ultraviolet irradiation device whose temperature is controlled to about 100 ° C., which is lower than the preheating temperature, to crosslink and cure the resist resin.
その後、サファイア基板11を予備加熱の温度よりも高い150℃程度に加熱し、予備加熱で除去しきれなかったレジスト15中の有機溶剤を完全に除去する。予備加熱時に高温で処理すれば、有機溶剤を完全に除去することができるが、その後のパターンの露光等の処理に悪影響を与え、所望のフォトレジストパターン16が形成できなくなる可能性があるため、2段階で加熱することが好ましい。 Thereafter, the sapphire substrate 11 is heated to about 150 ° C., which is higher than the preheating temperature, and the organic solvent in the resist 15 that could not be removed by the preheating is completely removed. If it is processed at a high temperature during preheating, the organic solvent can be completely removed, but it may adversely affect the subsequent processing such as exposure of the pattern, and the desired photoresist pattern 16 may not be formed. Heating in two stages is preferred.
続いて、プラズマエッチング装置にサファイア基板11を入れ、Cl2ガス、BCl3ガス、及びArガス等を供給した後、プラズマを生成し、サファイア基板11のエッチングを行うと、微小凸部12が形成される(図3(c))。 Subsequently, the sapphire substrate 11 is placed in a plasma etching apparatus, Cl 2 gas, BCl 3 gas, Ar gas, and the like are supplied, and then plasma is generated and the sapphire substrate 11 is etched to form minute protrusions 12. (FIG. 3C).
このとき、例えば、エッチング時間を長くすることで、微小凸部12に徐々に傾斜面が形成されていくと共に、その傾斜面がなだらかになっていく(図3(d)〜(f))。つまり、エッチング時間等のエッチングの条件を調整することにより、微小凸部12の傾斜面の角度を調整することが可能である。 At this time, for example, by increasing the etching time, an inclined surface is gradually formed on the minute convex portion 12, and the inclined surface becomes gentle (FIGS. 3D to 3F). That is, it is possible to adjust the angle of the inclined surface of the minute convex portion 12 by adjusting the etching conditions such as the etching time.
このようにして、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積の5%以上の割合を占めるように、微小凸部12の傾斜面の角度を調整する。 In this way, the region 13 within ± 10 degrees from the surface of the sapphire substrate 11 facing the a-axis direction and having an angle of 43.2 degrees from the C plane as a reference plane is 5% or more of the surface area of the micro-projections 12. The angle of the inclined surface of the minute convex portion 12 is adjusted so as to occupy the ratio.
これらの方法により、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積に占める割合をエッチング時間を調整することにより0%から50%まで調整して、得られた窒化ガリウム結晶成長用サファイア基板上にそれぞれ窒化ガリウム結晶を成長させた。そして、それぞれの窒化ガリウム結晶についてR面とC面におけるX線ロッキングカーブの半値幅を測定したところ、表1及び図4に示すような結果が得られた。 By these methods, the ratio of the region 13 within ± 10 degrees to the surface area of the micro-projections 12 with the surface of the sapphire substrate 11 facing the a-axis direction and having an angle from the C plane of 43.2 degrees as a reference plane is calculated. The gallium nitride crystal was grown on the sapphire substrate for gallium nitride crystal growth obtained by adjusting the etching time from 0% to 50%. And when the half width of the X-ray rocking curve in R surface and C surface was measured about each gallium nitride crystal, the result as shown in Table 1 and FIG. 4 was obtained.
表1及び図4から分かるように、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積に占める割合が5%未満である場合には、X線ロッキングカーブの半値幅が大きく、5%以上である場合には割合が高いほどX線ロッキングカーブの半値幅が小さくなっている。 As can be seen from Table 1 and FIG. 4, the region 13 within ± 10 degrees from the surface of the sapphire substrate 11 facing the a-axis direction and having an angle from the C plane of 43.2 degrees as a reference plane is the minute protrusion 12. When the proportion of the surface area is less than 5%, the full width at half maximum of the X-ray rocking curve is large. When the proportion is 5% or more, the full width at half maximum of the X-ray rocking curve is small.
割合が5%未満であると、窒化ガリウム結晶の成長中にそのR面が消失し、成長の早い段階で窒化ガリウム結晶の表面が平坦化されてしまい、その他の面が窒化ガリウム結晶の成長に対して優勢となるため、前述したような効果を得ることができなかったものと考えられる。 If the ratio is less than 5%, the R plane disappears during the growth of the gallium nitride crystal, the surface of the gallium nitride crystal is flattened at an early stage of growth, and the other plane is used for the growth of the gallium nitride crystal. It is presumed that the effect as described above could not be obtained because it became dominant.
よって、サファイア基板11のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域13が微小凸部12の表面積に占める割合が5%以上となるように調整する。 Therefore, the ratio of the area 13 within ± 10 degrees to the surface area of the micro-projections 12 is 5% or more with the surface of the sapphire substrate 11 facing the a-axis direction and the angle of 43.2 degrees from the C plane as a reference plane. Adjust so that
これまで説明してきた構造の窒化ガリウム結晶成長用サファイア基板10を用いて、その上に窒化ガリウム結晶14を成長させると、従来に比べて窒化ガリウム結晶14の更なる低転位化を実現でき、窒化ガリウム結晶14のより一層の高品質化が可能となる。 When the gallium nitride crystal 14 is grown on the sapphire substrate 10 for growing a gallium nitride crystal having the structure described so far, the dislocation of the gallium nitride crystal 14 can be further reduced as compared with the conventional case. The quality of the gallium crystal 14 can be further improved.
従って、本発明によれば、従来に比べて窒化ガリウム結晶の更なる低転位化を実現し、窒化ガリウム結晶のより一層の高品質化を可能とする窒化ガリウム結晶成長用サファイア基板、窒化ガリウム結晶の製造方法、及び窒化ガリウム結晶を提供することができる。 Therefore, according to the present invention, the gallium nitride crystal growth sapphire substrate, gallium nitride crystal, which realizes further lower dislocations of the gallium nitride crystal than the prior art and enables higher quality of the gallium nitride crystal. And a gallium nitride crystal can be provided.
なお、本実施の形態では、フォトレジストパターン16を六角形パターンとしたが、円形パターンで形成しても構わない。 In this embodiment, the photoresist pattern 16 is a hexagonal pattern, but it may be a circular pattern.
10 窒化ガリウム結晶成長用サファイア基板
11 サファイア基板
12 微小凸部
13 領域
14 窒化ガリウム結晶
15 レジスト
16 フォトレジストパターン
DESCRIPTION OF SYMBOLS 10 Sapphire substrate for gallium nitride crystal growth 11 Sapphire substrate 12 Minute convex portion 13 Region 14 Gallium nitride crystal 15 Resist 16 Photoresist pattern
Claims (3)
前記サファイア基板のa軸方向を向きC面からの角度が43.2度の面を基準面としてそこから±10度以内の領域が前記微小凸部の表面積の5%以上の割合を占めることを特徴とする窒化ガリウム結晶成長用サファイア基板。 In the sapphire substrate for gallium nitride crystal growth in which a plurality of minute protrusions are formed on the C surface of the sapphire substrate,
The surface of the sapphire substrate facing the a-axis direction and having an angle of 43.2 degrees from the C plane as a reference plane, a region within ± 10 degrees occupies a ratio of 5% or more of the surface area of the micro-projections. A sapphire substrate for gallium nitride crystal growth.
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