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CN1818798A - Method and device for producing photon crystal mask layer on LED - Google Patents

Method and device for producing photon crystal mask layer on LED Download PDF

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CN1818798A
CN1818798A CNA2006100498506A CN200610049850A CN1818798A CN 1818798 A CN1818798 A CN 1818798A CN A2006100498506 A CNA2006100498506 A CN A2006100498506A CN 200610049850 A CN200610049850 A CN 200610049850A CN 1818798 A CN1818798 A CN 1818798A
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CN1818798B (en
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佘俊
敖献煜
何赛灵
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Zhejiang University ZJU
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Zhejiang University ZJU
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Abstract

A method for preparing photon crystal mask layer on LED includes dividing one laser beam to be three laser beams after said beam is space-filtered and extended as well as collimated, then focusing three laser beams on photo resist mask layer on LED chip surface by reflecting mirror, regulating incoming angle and intensity as well as polarization state of each laser beam to form set two-dimensional interference pattern, obtaining two-dimensional photon crystal mask after exposure and development .The device for realizing said method is also disclosed .

Description

Method and device for manufacturing photonic crystal mask layer on light emitting diode
Technical Field
The invention relates to a method and a device for manufacturing a photonic crystal mask layer, in particular to a method and a device for optimally designing a two-dimensional photonic crystal cladding mask on a light-emitting diode by utilizing a laser multi-beam interference technology.
Background
In recent years, high brightness Light Emitting Diodes (LEDs) have shown great competitiveness in the field of solid state lighting technology. Compared with the traditional lighting source, the LED has the advantages of low energy consumption, small size, long service life and the like, and the industrialization development is very rapid. The key issue in the research of LEDs is how to improve the luminous efficiency of LEDs, so as to reduce energy consumption and improve service life. In the existing industrialized LED products, although the internal quantum efficiency of the LED is close to 100%, most of the generated photons are limited by the phenomena of total reflection and lateral wave guiding, and are absorbed by the high refractive index material, and cannot be effectively transmitted out of the component, and cannot contribute to illumination (the extraction efficiency is low). Therefore, it is very urgent to find an effective way to improve the light emitting efficiency of the LED by improving the extraction efficiency.
As one of the most important achievements in the field of modern photonics, photonic crystals (photonics crystals) can effectively control the behavior of light. Photonic crystals are artificially created periodic structures [ j.d. joannopoulos, Photonic crystals: molding the flow of light, Princeton, 1995], a two-dimensional periodic structure made of dielectric materials such as silicon dioxide, silicon, gallium nitride, etc., or an array of metal pillars distributed two-dimensionally and periodically in a dielectric background. The two-dimensional periodicity means that the connecting line of the centers of any adjacent three pillars in the array forms a square lattice of an isosceles right triangle, or forms a triangular lattice of an equilateral triangle, and the like. The length of the shortest link is called the lattice constant.
In a conventional LED, a photonic crystal cladding structure is introduced, and the light energy of a guided wave mode which is captured by a cladding material with a High refractive index in a general LED structure and cannot contribute to illumination is converted into a leaky mode to be released as much as possible by utilizing the characteristics of a forbidden band of the photonic crystal [ s.fan, p.p.Villeneuve and J.D.Joannopolis, High efficiency conductivity of spectral emission from substrates of photonic crystals, Phys.Rev.Lett.783294, 1997 ]. Manufacturers of light emitting diodes have the opportunity to manipulate the behavior of photons, which can greatly increase the luminous efficiency of semiconductor LEDs and improve the light output characteristics.
At present, a two-dimensional periodic photonic crystal cladding mask is usually fabricated on an LED by an electron beam etching method, and then a photonic crystal cladding structure is etched on a semiconductor by inductively coupled plasma etching (ICP) and Reactive Ion Etching (RIE). The manufacturing method of the mask is slow in speed and high in cost, and cannot meet the requirement of large-scale industrialization.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a method and a device for preparing a photonic crystal cladding mask based on a laser multi-beam interference technology, which can meet the requirement of large-scale mold industrialization, and is quick, flexible and cheap.
The method comprises the steps of carrying out spatial filtering, beam expanding and collimation on a laser beam, then dividing the laser beam into three laser beams, converging the three laser beams on a photoresist mask layer on the surface of a light-emitting diode chip by a reflector, adjusting the incidence angle of each laser beam according to the set lattice point matrix of each interference pattern, adjusting the intensity and the polarization state of each laser beam according to the contrast of the set interference pattern and the facula pattern of each unit to form a set two-dimensional interference pattern, and carrying out exposure and development to obtain the two-dimensional photonic crystal mask.
The adjustment of the incident angle of each laser beam is based on the pre-designed lattice pattern of the two-dimensional photonic crystal, and the adjustment of the polar angle theta of each laser beam and the azimuth angle phi of the laser beam according to the formula (1)m,(m=1,2,3)。
<math> <mrow> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mi>sin</mi> <mi>&gamma;</mi> </mrow> <mrow> <mi>cos</mi> <mi>&gamma;</mi> <mo>-</mo> <mi>b</mi> <mo>/</mo> <mi>a</mi> </mrow> </mfrac> </mrow> </math>
φ1=2γ-φ2 (1)
φ3=-φ2
<math> <mrow> <mi>&theta;</mi> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mi>&lambda;</mi> <mo>/</mo> <mi>b</mi> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> <mi>sin</mi> <mi>&gamma;</mi> </mrow> </mfrac> </mrow> </math>
Where a, b are the lattice constants of the two-dimensional photonic crystal and γ is the angle between the basis vectors of the lattice. The polar and azimuthal angles determine the wavevector of the non-coplanar three-beam laser,
<math> <mrow> <mover> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>cos</mi> <mi></mi> <mi>&phi;</mi> <mi>sin</mi> <msub> <mi>&theta;</mi> <mi>m</mi> </msub> <mo>,</mo> <mi>sin</mi> <msub> <mi>&phi;</mi> <mi>m</mi> </msub> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mi>cos</mi> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>m</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
the light intensity distribution after the interference of the three beams is written as:
<math> <mrow> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>c</mi> <mn>12</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>G</mi> <mn>12</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>23</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>G</mi> <mn>23</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mo></mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>13</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>G</mi> <mn>13</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein,
<math> <mrow> <mover> <msub> <mi>G</mi> <mi>lm</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mover> <msub> <mi>k</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>=</mo> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <mrow> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>,</mo> </mrow> <mo>&RightArrow;</mo> </mover> <mn>1</mn> <mo>&le;</mo> <mi>l</mi> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mn>3</mn> </mrow> </math>
<math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>
the intensity and the polarization state of each laser beam are adjusted according to a unit pattern of a pre-designed photonic crystal and a formula (3) to determine clm. From clmTo determine beam parameters to achieve a desired structure <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>l</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> I.e. the intensity and polarization state of the beam; at c0Minimum temporal contrast ratio V ═ I (I)max-Imin)/(Imax+Imin) At the maximum, the number of the first,
<math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
c0under the constraint condition <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mover> <mrow> <mo>&CenterDot;</mo> <msub> <mi>k</mi> <mi>l</mi> </msub> </mrow> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2,3</mn> </mrow> </math> And <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>&le;</mo> <mi>l</mi> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mn>3</mn> </mrow> </math> the lower minimum.
The device for realizing the method comprises the following steps: by laser output, along the optical axis, place beam expanding filter, collimating lens and beam splitter in proper order, laser divides into three bundles behind the beam splitter, corresponds every laser, has a speculum, along the optical axis of each laser after passing through the beam splitter, has placed polarization attenuation controller.
The invention can form a large-area high-quality two-dimensional photonic crystal mask layer on the whole chip only by one-time exposure and development. And a diffraction optical device is adopted to realize light splitting, so that the complexity of a light path structure is reduced, and the stability of the light path is improved. On the basis of computer numerical simulation and optimization design, the intensity and polarization state of each laser beam are independently controlled, and high-quality interference patterns are obtained. The reflector reflects the three laser beams to the surface of the chip, so that the device has high flexibility, and the requirement of producing a two-dimensional photonic crystal cladding structure suitable for LEDs with different wavelengths and high luminous efficiency can be met only by adjusting the angle of the reflector aiming at the lattice constants of different structures. The device used by the invention is simple, has high flexibility, low cost and high production speed, and is suitable for manufacturing the photonic crystal mask on the surface of the light-emitting diode on a large scale.
Drawings
FIG. 1 is a schematic view of the overall structure of the present invention;
fig. 2 is a schematic diagram of three laser beams incident on the surface of the photoresist.
Detailed Description
As shown in fig. 1, the device is provided with a laser 1, and a beam expanding filter 2 is arranged on an output optical axis of the laser 1 and is used for expanding and filtering light emitted by the laser 1; the collimating lens 3 is arranged on the output optical axis of the beam expanding filter 2 and is used for collimating the expanded laser,forming a parallel light beam; the diffraction beam splitter 4 splits the incident parallel light beam into three beams; each laser beam passes through a polarization attenuation controller 5, the intensity and the polarization state of each laser beam are adjusted on the basis of computer numerical simulation optimization design, then a reflector 6 reflects the laser beam to a photoresist layer 7 coated on the surface of a light-emitting diode chip 8 at a certain angle according to the design requirement, the exposure intensity and the exposure time are reasonably controlled, and an interference pattern is formed on the photoresist layer 7. After development, the interference pattern can be recorded on the photoresist layer 7 to form a mask layer that can be used to fabricate a two-dimensional periodic photonic crystal cladding layer. After being reflected by the reflecting mirror, the three laser beams are incident on the surface of the photoresist layer as shown in FIG. 2. The lattice of the interference pattern is formed by the polar angle theta and the azimuth angle phi of the reflected three laser beamsmAnd (6) determining. The contrast of the interference pattern and the speckle pattern of each cell are determined by the intensity and polarization of the three lasers. The wavelength of the laser 1 used corresponds to the absorption wavelength of the photoresist used.
For example, to make a two-dimensional periodic triangular lattice photonic crystal mask, in order to obtain a two-dimensional periodic triangular lattice structure, the non-coplanar three laser beams should have azimuth angles of phi respectively1=0,φ2=120°,φ3120 DEG, and a polar angle theta sin-10.667 lambda/a. Wave vector of light beam of <math> <mrow> <mover> <msub> <mi>k</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mi>&lambda;</mi> <mo>[</mo> <mo>-</mo> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mi>cos</mi> <mi>&theta;</mi> <mo>]</mo> <mo>,</mo> </mrow> </math> <math> <mrow> <mover> <msub> <mi>k</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mi>&lambda;</mi> <mo>[</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mo>-</mo> <msqrt> <mn>3</mn> </msqrt> <mo>/</mo> <mn>2</mn> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mi>cos</mi> <mi>&theta;</mi> <mo>]</mo> <mo>,</mo> </mrow> </math> <math> <mrow> <mover> <msub> <mi>k</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mi>&lambda;</mi> <mo>[</mo> <mn>1</mn> <mo>/</mo> <mn>2</mn> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <msqrt> <mn>3</mn> </msqrt> <mo>/</mo> <mn>2</mn> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mi>cos</mi> <mi>&theta;</mi> <mo>]</mo> </mrow> </math> The interference occurs, and the light intensity distribution after the interference of the three beams can be written as follows:
<math> <mrow> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mi>x</mi> <mo>,</mo> <mi>y</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>+</mo> <mn>2</mn> <msub> <mi>c</mi> <mn>12</mn> </msub> <mi>cos</mi> <mo>[</mo> <mfrac> <mrow> <mn>4</mn> <mi>&pi;</mi> </mrow> <mrow> <msqrt> <mn>3</mn> </msqrt> <mi>a</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>x</mi> <msqrt> <mn>3</mn> </msqrt> <mo>/</mo> <mn>2</mn> <mo>-</mo> <mi>y</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mo>&CenterDot;</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <mo>+</mo> <mn>2</mn> <msub> <mi>c</mi> <mn>13</mn> </msub> <mi>cos</mi> <mo>[</mo> <mfrac> <mrow> <mn>4</mn> <mi>&pi;</mi> </mrow> <mrow> <msqrt> <mn>3</mn> </msqrt> <mi>a</mi> </mrow> </mfrac> <mrow> <mo>(</mo> <mi>x</mi> <msqrt> <mn>3</mn> </msqrt> <mo>/</mo> <mn>2</mn> <mo>+</mo> <mi>y</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>]</mo> <mo>+</mo> <mn>2</mn> <msub> <mi>c</mi> <mn>23</mn> </msub> <mi>cos</mi> <mo>[</mo> <mfrac> <mrow> <mn>4</mn> <mi>&pi;</mi> </mrow> <mrow> <msqrt> <mn>3</mn> </msqrt> <mi>a</mi> </mrow> </mfrac> <mi>y</mi> <mo>]</mo> </mrow> </math>
wherein <math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>,</mo> </mrow> </math> <math> <mrow> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>=</mo> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>&RightArrow;</mo> </mover> <mo>,</mo> <mn>1</mn> <mo>&le;</mo> <mi>l</mi> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mn>3</mn> <mo>.</mo> </mrow> </math>
And exposing and developing the photoresist under the interference light spots to obtain a two-dimensional periodic structure mask. Generally, when the unit pattern of the photonic crystal is set, c in the formula (5) can be determinedlm
In order to maximize the contrast of the interference pattern, the appropriate configuration parameters, i.e., the polarization and intensity of the light beam, need to be selected. We composed of clmTo determine beam parameters to achieve a desired structure <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>l</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> At the same time, make c0Minimum (corresponding to the background intensity of the interference spot) so that the contrast V ═ Imax-Imin)/(Imax+Imin)(IminMinimum light intensity, ImaxMaximum light intensity). When all constants clm(1. ltoreq. l. ltoreq. m. ltoreq.3) minimum c0The maximum V is meant. Thus, the problem becomes how to make
<math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>
Under the constraint condition <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msub> <mi>k</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mi>l</mi> <mo>=</mo> <mn>1,2,3</mn> </mrow> </math> And <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>,</mo> <mn>1</mn> <mo>&le;</mo> <mi>l</mi> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mn>3</mn> </mrow> </math> the lower minimum. Thus becomes a nonlinear gauge with nonlinear constraintThe problem can be solved by Sequential Quick Programming (SQP) method, MatlabTMThis procedure is provided.

Claims (2)

1. The method for manufacturing the photonic crystal mask layer on the light-emitting diode is characterized in that a beam of laser is divided into three beams after being subjected to spatial filtering, beam expanding and collimation, then the three beams of laser are converged on the photoresist mask layer on the surface of the light-emitting diode chip by a reflector, the incident angle of each beam of laser is respectively adjusted according to the set lattice of an interference pattern, the intensity and the polarization state of each beam of laser are respectively adjusted according to the set contrast of the interference pattern and the light spot pattern of each unit to form a set two-dimensional interference pattern, and the two-dimensional photonic crystal mask is obtained after exposure and development;
the adjustment of the incident angle of each laser beam is based on the pre-designed lattice pattern of the two-dimensional photonic crystal, and the adjustment of the polar angle theta of each laser beam and the azimuth angle phi of the laser beam according to the formula (1)m(m=1,2,3)
<math> <mrow> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> <mo>=</mo> <msup> <mi>tan</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mi>sin</mi> <mi>&gamma;</mi> </mrow> <mrow> <mi>cos</mi> <mi>&gamma;</mi> <mo>-</mo> <mi>b</mi> <mo>/</mo> <mi>a</mi> </mrow> </mfrac> </mrow> </math>
<math> <mrow> <msub> <mi>&phi;</mi> <mn>1</mn> </msub> <mo>=</mo> <mn>2</mn> <mi>&gamma;</mi> <mo>-</mo> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> </mrow> </math>
<math> <mrow> <msub> <mi>&phi;</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>-</mo> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> </mrow> </math>
<math> <mrow> <mi>&theta;</mi> <mo>=</mo> <msup> <mi>sin</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mfrac> <mrow> <mi>&gamma;</mi> <mo>/</mo> <mi>b</mi> </mrow> <mrow> <mn>2</mn> <mi>sin</mi> <msub> <mi>&phi;</mi> <mn>2</mn> </msub> <mi>sin</mi> <mi>&gamma;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </math>
Wherein a and b are lattice constants of the two-dimensional photonic crystal, and gamma is an included angle between lattice basis vectors; the polar and azimuthal angles determine the wavevector of the non-coplanar three-beam laser,
<math> <mrow> <mover> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>2</mn> <mi>&pi;</mi> <mo>/</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>cos</mi> <mi>&phi;</mi> <msub> <mrow> <mi>sin</mi> <mi>&theta;</mi> </mrow> <mi>m</mi> </msub> <mo>,</mo> <msub> <mrow> <mi>sin</mi> <mi>&phi;</mi> </mrow> <mi>m</mi> </msub> <mi>sin</mi> <mi>&theta;</mi> <mo>,</mo> <mi>cos</mi> <mi>&theta;</mi> <mo>)</mo> </mrow> <mo>,</mo> <mrow> <mo>(</mo> <mi>m</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow> </math>
the light intensity distribution after the interference of the three beams is as follows:
<math> <mrow> <msub> <mi>I</mi> <mn>0</mn> </msub> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>c</mi> <mn>12</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>G</mi> <mn>12</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>23</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <mrow> <msub> <mi>G</mi> <mn>23</mn> </msub> <mo>&CenterDot;</mo> </mrow> <mo>&RightArrow;</mo> </mover> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>c</mi> <mn>13</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mover> <msub> <mi>G</mi> <mn>13</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow> </math>
wherein,
<math> <mrow> <mover> <msub> <mi>G</mi> <mi>lm</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mrow> <mo>(</mo> <mover> <msub> <mi>k</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>-</mo> <mover> <msub> <mi>k</mi> <mi>m</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>=</mo> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>&RightArrow;</mo> </mover> <mo>,</mo> <mn>1</mn> <mo>&le;</mo> <mi>l</mi> <mo>&le;</mo> <mi>m</mi> <mo>&le;</mo> <mn>3</mn> </mrow> </math>
<math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> </mrow> </math>
the intensity and the polarization state of each laser beam are adjusted according to a unit pattern of a pre-designed photonic crystal and a formula (3) to determine clm(ii) a From clmTo determine beam parameters to achieve a desired structure <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mrow> <mo>(</mo> <mover> <mi>r</mi> <mo>&RightArrow;</mo> </mover> <mo>)</mo> </mrow> <mrow> <mo>(</mo> <mi>l</mi> <mo>=</mo> <mn>1,2,3</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow> </math> I.e. the intensity and polarization state of the beam; at c0Minimum temporal contrast ratio V ═ I (I)max-Imin)/(Imax+Imin) At the maximum, the number of the first,
<math> <mrow> <msub> <mi>c</mi> <mn>0</mn> </msub> <mo>=</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>1</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>2</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>|</mo> <mover> <msub> <mi>E</mi> <mn>3</mn> </msub> <mo>&RightArrow;</mo> </mover> <mo>|</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow> </math>
c0under the constraint condition <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msub> <mi>k</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mrow> </math> 1, 2, 3 and <math> <mrow> <mover> <msub> <mi>E</mi> <mi>l</mi> </msub> <mo>&RightArrow;</mo> </mover> <mo>&CenterDot;</mo> <mover> <msubsup> <mi>E</mi> <mi>m</mi> <mo>*</mo> </msubsup> <mo>&RightArrow;</mo> </mover> <mo>=</mo> <msub> <mi>c</mi> <mi>lm</mi> </msub> <mo>,</mo> </mrow> </math> l is more than or equal to 1 and less than or equal to m is less than or equal to 3.
2. The apparatus used in the method of claim 1, wherein the laser, the beam expanding filter, the collimating lens and the beam splitter are sequentially arranged along the optical axis, the reflecting mirrors are respectively arranged at the positions corresponding to the three laser beams passing through the beam splitter, and the polarization attenuation controller is arranged along the optical axis of each laser beam passing through the beam splitter.
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