CN102375914A - Method for improving C-wave band LED emergent light efficiency by using two-dimensional photon crystal - Google Patents

Abstract

The invention discloses a method for improving C-wave band LED emergent light efficiency by using a two-dimensional photon crystal. The method comprises the steps of: 1, based on a finite different time domain (FDTD) algorithm theory, constructing a two-dimensional photon crystal structure model; analyzing a two-dimensional photon crystal band structure based on the FDTD algorithm; and 3, selecting an optimal band structure and completing the design of two-dimensional photon crystal parameters. In the invention, the band solution is carried out on the two-dimensional photon crystal structure model by adopting the FDTD algorithm, two-dimensional photon crystal structure and parameters for improving the C-wave band LED emergent efficiency are designed. Through simulation calculation, the C-wave band LED emergent efficiency can be increased by the two-dimensional photon crystal structure and parameters provided by the invention.

Description

A kind of method of utilizing 2 D photon crystal to improve C-band LED light extraction efficiency

Technical field

The invention belongs to the photoelectron technology field, be specifically related to C-band LED light extraction efficiency, utilize Finite Difference-Time Domain to divide algorithm that the 2 D photon crystal band structure is found the solution, design the two-dimensional photon crystal structure parameter that is suitable for improving C-band LED light extraction efficiency.

Background technology

Fiber grating sensing technology be accompanied by light transmitting fiber and Fibre Optical Communication Technology and develop rapidly a kind of be carrier with light, optical fiber is ature of coal, the novel sensing technology of perception and transmission outer signals (measured).It has anti-electromagnetic interference (EMI), highly sensitive, safe and reliable, corrosion-resistant, can carry out distributed measurement, be convenient to plurality of advantages such as networking, be in recent years high-tech application technology with fastest developing speed in the world.Since the seventies in 20th century; The application of fiber grating sensing technology has progressively developed into each industrial circles such as electric power, oil, petrochemical industry, traffic and building from military field, in great safety monitoring fields such as public safety, national defence, industrial or agricultural safety in production, environmental protection important application is arranged also.

Owing to the light extraction efficiency of the C-band led light source that is used for optical fiber grating sensing at present is lower, limited led light source and further used in the optical fiber grating sensing field.The low main cause of LED light extraction efficiency is: the refractive index of the semiconductor material refractive index ratio air of LED active layer is high; Total reflection can take place at the interface of LED medium and air in light; Most of light not only can not emit from LED; And absorbed by hard contact, substrate or active layer, can produce heat energy or cause electronics and hole radiationless compound, cause light extraction efficiency to receive very big restriction.

Aspect raising LED light extraction efficiency, the scientific research personnel has done multiple trial, as adopting inverted pyramid shape structure, growth distribution formula Bragg reflecting layer, making the membrane structure of transparent substrates, surface roughening etc.Though they all play improvement effect in various degree to light extraction efficiency, effect is still undesirable.Surface coarsening technology is through increasing light escape angle, light extraction efficiency is promoted to about 65%, if more further with silicones or similarly transparent material encapsulation, light extraction efficiency can be up to 80%.Though can improve light extraction efficiency through encapsulation,, so can sacrifice the brightness of LED because the refraction coefficient of the brightness of LED and encapsulating material square is inversely proportional to.

The present invention solves the problem of C-band LED light extraction efficiency; With Finite Difference-Time Domain branch theory is that the two-dimensional photon crystal structure model is set up on the basis; Designed the two-dimensional photon crystal structure of square arrangement and triangle arrangement; And utilize Finite Difference-Time Domain to divide algorithm that the band structure of the 2 D photon crystal of different lattice constants, different duty is found the solution, and design the parameters of the 2 D photon crystal that is used to improve C-band LED light extraction efficiency, the General layout Plan schematic flow sheet is as shown in Figure 1.

Summary of the invention

The objective of the invention is to solve the problem of C-band LED light extraction efficiency; Through being that the two-dimensional photon crystal structure model is set up on the basis with Finite Difference-Time Domain branch theory; Designed the two-dimensional photon crystal structure of square arrangement and triangle arrangement; Utilize Finite Difference-Time Domain to divide algorithm that the band structure of the 2 D photon crystal of different lattice constants, different duty is found the solution, select optimum photonic crystal band structure, design the two-dimensional photon crystal structure parameter that can improve C-band LED light extraction efficiency.

A kind of method of utilizing 2 D photon crystal to improve C-band LED light extraction efficiency realizes, may further comprise the steps:

(1) divide algorithm to be the basis with Finite Difference-Time Domain, make up the two-dimensional photon crystal structure model, comprising the two-dimensional photon crystal structure of pros' arrangement and the two-dimensional photon crystal structure of triangle arrangement, structure is like Fig. 3, shown in 5.A is the grating constant of 2 D photon crystal among Fig. 3,5, and r is the medium post/airport radius of 2 D photon crystal, dutycycle Rp=r/a.

(2) divide finding the solution of algorithm 2 D photon crystal band structure based on Finite Difference-Time Domain, found the solution the band structure of the 2 D photon crystal of different lattice constants, different duty.At first Maxwell's differential equation group is launched under rectangular coordinate system; Be converted into difference equation again; And then on time and space, progressively find the solution electric field and magnetic field; Calculate the band structure of photonic crystal, we have found the solution the band structure of the 2 D photon crystal of different lattice constants, different duty.

(3) choose optimum band structure, and can be with the 2 D photon crystal parameter of confirming to be used to improve C-band LED light extraction efficiency, choose the optimum principle that can be with and be according to optimum 2 D photon crystal:

1,2 D photon crystal can be with band gap width enough big, can be used for improving the light extraction efficiency of broad wavelength coverage;

2, based on selecting optimum can be with frequency, accomplish optimum band structure design with frequency f and the relational expression f=a/ λ that can improve the lattice paprmeter a of light extraction efficiency wavelength X and 2 D photon crystal.

Through optimum band structure, can be met in the 2 D photon crystal parameter that improves C-band LED light extraction efficiency, concrete parameter comprises: the grating constant a of photonic crystal, dutycycle Rp and structure cell radius r.

Description of drawings

Fig. 1 is that the present invention utilizes 2 D photon crystal to improve C-band LED light extraction efficiency schematic flow sheet;

Fig. 2 is the square 2 D photon crystal lattice vector structural representation of arranging;

Fig. 3 is the square two-dimensional photon crystal structure synoptic diagram of arranging;

Fig. 4 is a triangle arrangement 2 D photon crystal lattice vector structural representation;

Fig. 5 is a triangle arrangement two-dimensional photon crystal structure synoptic diagram;

Fig. 6 is that square photonic crystal when arranging medium post and a=500nm, Rp=0.3 can be with synoptic diagram;

Photonic crystal when Fig. 7 is triangle arrangement airport and a=500nm, Rp=0.44 can be with synoptic diagram;

Photonic crystal when Fig. 8 is triangle arrangement medium post and a=500nm, Rp=0.35 can be with synoptic diagram.

Embodiment

Be described in detail most preferred embodiment of the present invention below in conjunction with technical scheme.

The objective of the invention is to solve the problem of C-band LED light extraction efficiency; Through being that the two-dimensional photon crystal structure model is set up on the basis with Finite Difference-Time Domain branch theory; Designed the two-dimensional photon crystal structure of square arrangement and triangle arrangement; Utilize Finite Difference-Time Domain to divide algorithm that the band structure of the 2 D photon crystal of different lattice constants, different duty is found the solution; Select optimum photonic crystal band structure, design the two-dimensional photon crystal structure parameter that is used to improve C-band LED light extraction efficiency, it comprises the steps:

1, the design of two-dimensional photon crystal structure

Dividing algorithm with Finite Difference-Time Domain is theoretical foundation, makes up the two-dimensional photon crystal structure model, comprising the two-dimensional photon crystal structure of pros' arrangement and the two-dimensional photon crystal structure of triangle arrangement, mainly contains following step:

(1) basic parameter design, comprising: the integral multiple of photonic crystal lattice constant is generally selected in the design of global parameter, boundary parameter and zoning, zoning, in order accurately to solve the band structure of photonic crystal, boundary condition selection cycle border.

(2) design of material comprises the specific inductive capacity and the characteristics design of material, and the specific inductive capacity of material to choose be the material decision according to LED.

(3) structure and element design comprise: the radius of photonic crystal structure cell and highly design, the height of photonic crystal is generally chosen 100-200nm.

(4) design of square arrangement of completion and triangle arrangement two-dimensional photon crystal structure.The design of photonic crystal array will be accomplished according to the lattice vector of photonic crystal, and the lattice vector of the square photonic crystal of arranging is as shown in Figure 2, and wherein Ka is the lattice vector on the specify columns direction, and Kb is the lattice vector on nominated bank's direction.With Ka and Kb respectively to X axle and Y axial projection; And establishing photonic crystal lattice constant is a, then Ka and Kb are respectively wherein

be respectively the unit vector of X, Y direction.Therefore, for the two-dimensional photon crystal structure that pros arrange, the numerical value of lattice vector Ka on directions X on the column direction is a, and the numerical value on the Y direction is 0; In like manner can get, the numerical value of lattice vector Kb on directions X on the line direction is 0, and the numerical value on the Y direction is a.Further design is gone and the span that is listed as again, can accomplish square design of arranging the 2 D photon crystal array.The two-dimensional photon crystal structure that the pros that design obtains arrange is as shown in Figure 3, and a is the grating constant of 2 D photon crystal among the figure, and r is the medium post/airport radius of 2 D photon crystal, dutycycle Rp=r/a.

For the 2 D photon crystal array of triangle arrangement, its lattice vector is as shown in Figure 4, and wherein Ka is the lattice vector on the specify columns direction, and Kb is the lattice vector on nominated bank's direction.With Ka and Kb respectively to X axle and Y axial projection; And establish the value a of photonic crystal lattice constant, then Ka and Kb are respectively

wherein

be respectively the unit vector of X, Y direction.Therefore, for the two-dimensional photon crystal structure of triangle arrangement, the numerical value of lattice vector Ka on directions X on the column direction is a, and the numerical value on the Y direction is 0; In like manner can get; The numerical value of lattice vector Kb on directions X on the line direction is a/2; Numerical value on the Y direction is

further designs row and the span that is listed as again, can accomplish the design of triangle arrangement 2 D photon crystal array.The two-dimensional photon crystal structure of the triangle arrangement that design obtains is as shown in Figure 5, and a is the grating constant of 2 D photon crystal among the figure, and r is the medium post/airport radius of 2 D photon crystal, dutycycle Rp=r/a.

2, divide finding the solution that the algorithm 2 D photon crystal can be with based on Finite Difference-Time Domain

The band structure of utilizing Finite Difference-Time Domain to divide algorithm to find the solution 2 D photon crystal, we at first launch Maxwell's differential equation group to obtain under rectangular coordinate system:

$\left\{\begin{array}{c}\frac{\∂E_z}{\∂y}-\frac{\∂E_y}{\∂z}=-\mathrm{\μ}\frac{\∂H_x}{\∂t}-{\mathrm{\σ}}_m{H}_x\\ \frac{\∂E_x}{\∂z}-\frac{\∂E_z}{\∂x}=-\mathrm{\μ}\frac{\∂H_y}{\∂t}-{\mathrm{\σ}}_m{H}_y\\ \frac{\∂E_y}{\∂x}-\frac{\∂E_x}{\∂y}=-\mathrm{\μ}\frac{\∂H_z}{\∂t}-{\mathrm{\σ}}_m{H}_z\end{array}\right.---\left(1\right)$

And:

$\left\{\begin{array}{c}\frac{\∂H_z}{\∂y}-\frac{\∂H_y}{\∂z}=-\mathrm{\ϵ}\frac{\∂E_x}{\∂t}-\mathrm{\σ}{E}_x\\ \frac{\∂H_x}{\∂z}-\frac{\∂H_z}{\∂x}=-\mathrm{\ϵ}\frac{\∂E_y}{\∂t}-\mathrm{\σ}{E}_y\\ \frac{\∂H_y}{\∂x}-\frac{\∂H_x}{\∂y}=-\mathrm{\ϵ}\frac{\∂E_z}{\∂t}-\mathrm{\σ}{E}_z\end{array}\right.---\left(2\right)$

ε in the following formula, σ, μ are respectively the dielectric coefficients of medium, conductivity, unit permeance.In three dimensions, if establish observation point (x, y, z) be Ex node (k), and moment t=(n+1) Δ t, then the solving equation of electric field component Ex can disperse and be for i+1/2, j: $E_x^{n+1}(i+1/2,j,k)=\mathrm{CA}\left(m\right)\·E_x^n(i+1/2,j,k)$

$+\mathrm{CB}\left(m\right)\·\left[\begin{array}{c}\frac{H_z^{n+1/2}(i+1/2,j+1/2,k)-H_z^{n+1/2}(i+1/2,j-1/2,k)}{\mathrm{\Δy}}\\ -\frac{H_y^{n+1/2}(i+1/2,j,k+1/2)-H_y^{n+1/2}(i+1/2,j,k-1/2)}{\mathrm{\Δz}}\end{array}\right]---\left(3\right)$

In the formula: $\mathrm{CA}\left(m\right)=\frac{1-\frac{\mathrm{\σ}\left(m\right)\mathrm{\Δ\; t}}{2\mathrm{\ϵ}\left(m\right)}}{1+\frac{\mathrm{\σ}\left(m\right)\mathrm{\Δ\; t}}{2\mathrm{\ϵ}\left(m\right)}}---\left(4\right)$

$\mathrm{CB}\left(m\right)=\frac{\frac{\mathrm{\Δt}}{\mathrm{\ϵ}\left(m\right)}}{1+\frac{\mathrm{\σ}\left(m\right)\mathrm{\Δt}}{2\mathrm{\ϵ}\left(m\right)}}---\left(5\right)$

(k), other field component solution procedure is similar for i+1/2, j for label m=in the following formula.We can solve the band structure of 2 D photon crystal according to these difference equations.

3, choose optimum band structure, accomplish the design of 2 D photon crystal parameter

No matter be the square two-dimensional photon crystal structure of arranging or the two-dimensional photon crystal structure of triangle arrangement, the band gap of its band structure all can change along with the variation of photonic crystal dutycycle Rp.We according to the influence of different Rp to band gap, find out best Rp and normalized frequency f (a/ λ) and normalization centre frequency f through the change to two-dimensional photon crystal structure ₀Thereby, obtain the optimal parameter of photonic crystal.

Through changing the parameter of 2 D photon crystal, found the solution being with of the two-dimentional airport photon crystal structure of square arrangement, square arrangement two-dimensional medium post photon crystal structure, triangle arrangement two dimension airport photon crystal structure and triangle arrangement two-dimensional medium post photon crystal structure; Every kind of structure solves the photonic crystal band structure of identical grating constant different duty and same duty cycle different lattice constants again simultaneously, thereby selects optimum photonic crystal band structure.

Be that 500nm is an example below with the grating constant, being with of photonic crystal of the different structure that solves analyzed.Find that through finding the solution us there is not band gap in the band structure of the square two-dimentional airport photonic crystal of arranging.Band structure when square arrangement medium post and grating constant a=500nm, dutycycle Rp=0.3 is as shown in Figure 6.It has three H polarization forbidden bands, and the normalized frequency scope is respectively 0.2249-0.2938,0.3978-0.5017,0.6156-0.6796; Energy gap is respectively 0.0689,0.1039, and 0.0640; The normalization centre frequency is respectively 0.25935,0.44975, and 0.6476.

Band structure when triangle arrangement airport and grating constant a=500nm, dutycycle Rp=0.44 is as shown in Figure 7.It has only an E polarization forbidden band, and the normalized frequency scope is 0.2448-0.4147, and energy gap is 0.1699, and the normalization centre frequency is 0.32975.

Band structure when triangle arrangement medium post and grating constant a=500nm, dutycycle Rp=0.35 is shown in Fig. 8 (a) and (b).It has an E polarization forbidden band and three H polarization forbidden bands, and the normalized frequency scope is respectively 0.2918-0.3358,0.2019-0.2578,0.3558-0.4257; 0.5256-0.5856 energy gap is respectively 0.0440,0.0559; 0.0699,0.0600, the normalization centre frequency is respectively 0.3138; 0.2299,0.3908,0.5556.

In all band structures, choose optimum can being with, the optimum selection principle that can be with is:

(1) 2 D photon crystal can be with band gap width enough big, can be used for improving the light extraction efficiency of broad wavelength coverage;

(2) according to can with frequency f with can improve the relational expression f=a/ λ of the grating constant a of light extraction efficiency wavelength X and 2 D photon crystal, selection can improve the optimum of C-band LED light extraction efficiency can be with frequency.

Can be with selection principle according to optimum, the optimum band structure of 2 D photon crystal of selecting to be used to improve C-band LED light extraction efficiency is as shown in Figure 7.It is a triangle arrangement airport two-dimensional photon crystal structure, and the normalized frequency scope is 0.2448-0.4147, and energy gap is 0.1699, and the normalization centre frequency is 0.32975, and can improve the emission wavelength scope is 1205-2042nm; Its corresponding photonic crystal parameters is: grating constant a=500nm, dutycycle Rp=0.44 and structure cell radius r=220nm.

Claims (4)

1. a method of utilizing 2 D photon crystal to improve C-band LED light extraction efficiency realizes, comprises the steps:

(1) is the basis with Finite Difference-Time Domain branch theory of algorithm; Made up the two-dimensional photon crystal structure model, it comprises: square two-dimentional airport photon crystal structure, square two-dimensional medium post photon crystal structure, triangle arrangement two dimension airport photon crystal structure and the triangle arrangement two-dimensional medium post photon crystal structure arranged arranged;

(2) divide the finding the solution of 2 D photon crystal band structure of algorithm based on Finite Difference-Time Domain; Through Maxwell's differential equation group is launched in rectangular coordinate system; The electromagnetic field that utilizes difference equation to find the solution two-dimensional photon crystal structure distributes, and draws the band structure of photonic crystal;

(3) choose optimum band structure, accomplish the design of 2 D photon crystal parameter, photonic crystal parameters comprises: the grating constant a of photonic crystal, dutycycle Rp and structure cell radius r.

2. the method for utilizing 2 D photon crystal to improve C-band LED light extraction efficiency according to claim 1 is characterized in that: divide algorithm for theoretical foundation designs the two-dimensional photon crystal structure model with Finite Difference-Time Domain, may further comprise the steps:

(1) grating constant and the dutycycle of design 2 D photon crystal material, photonic crystal medium post/airport radius, photonic crystal are accomplished the design of photonic crystal structure cell;

(2) according to a photonic crystal structure cell, design 2 D photon crystal array is accomplished the two-dimensional photon crystal structure design of square arrangement and triangle arrangement.

3. the method for utilizing 2 D photon crystal to improve C-band LED light extraction efficiency according to claim 1; It is characterized in that: the band structure of utilizing Finite Difference-Time Domain to divide algorithm to find the solution 2 D photon crystal, at first we launch Maxwell's differential equation group to obtain under rectangular coordinate system:

$\left\{\begin{array}{c}\frac{\∂E_z}{\∂y}-\frac{\∂E_y}{\∂z}=-\mathrm{\μ}\frac{\∂H_x}{\∂t}-{\mathrm{\σ}}_m{H}_x\\ \frac{\∂E_x}{\∂z}-\frac{\∂E_z}{\∂x}=-\mathrm{\μ}\frac{\∂H_y}{\∂t}-{\mathrm{\σ}}_m{H}_y\\ \frac{\∂E_y}{\∂x}-\frac{\∂E_x}{\∂y}=-\mathrm{\μ}\frac{\∂H_z}{\∂t}-{\mathrm{\σ}}_m{H}_z\end{array}\right.---\left(1\right)$

And:

$\left\{\begin{array}{c}\frac{\∂H_z}{\∂y}-\frac{\∂H_y}{\∂z}=-\mathrm{\ϵ}\frac{\∂E_x}{\∂t}-\mathrm{\σ}{E}_x\\ \frac{\∂H_x}{\∂z}-\frac{\∂H_z}{\∂x}=-\mathrm{\ϵ}\frac{\∂E_y}{\∂t}-\mathrm{\σ}{E}_y\\ \frac{\∂H_y}{\∂x}-\frac{\∂H_x}{\∂y}=-\mathrm{\ϵ}\frac{\∂E_z}{\∂t}-\mathrm{\σ}{E}_z\end{array}\right.---\left(2\right)$

ε in the following formula, σ, μ are respectively the dielectric coefficients of medium; Conductivity, unit permeance, we draw by formula (1), (2); In three dimensions, the electric field of this moment and magnetic field is alternately sampling on time sequencing, and the sample time interval is the phase difference of half time step each other; Constitute explicit difference equation after making Maxwell's vorticity equation discrete, thus iterative in time; Therefore, by the initial value and the boundary condition of given corresponding electromagnetic problems, what just can progressively advance finds the solution external electromagnetic field, and then finds the solution and obtain the 2 D photon crystal band structure.

4. based on the described method of utilizing 2 D photon crystal to improve C-band LED light extraction efficiency of claim 1; It is characterized in that:, select to be suitable for improving the optimum band structure of C-band LED light extraction efficiency based on the band structure of the 2 D photon crystal of the different lattice constants different duty of finding the solution;

Choosing the optimum principle that can be with is:

(1) 2 D photon crystal can be with band gap width enough big, can be used for improving the light extraction efficiency of broad wavelength coverage;

(2) based on selecting optimum can be with frequency, accomplish optimum band structure design with frequency f and the relational expression f=a/ λ that can improve the lattice paprmeter a of light extraction efficiency wavelength X and 2 D photon crystal;

According to optimum band structure, can be met in the 2 D photon crystal parameter that improves C-band LED light extraction efficiency, concrete parameter comprises: the grating constant a of photonic crystal, dutycycle Rp and structure cell radius r.

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