Numerical Analysis of Planar Light-Emitting Diodewith Designed p-Electrode

Irina Khmyrova1, Norikazu Watanabe1, Anatoly Kovalchuk2,Julia Kholopova2, and Sergei Shapoval2

1University of Aizu, Aizu-Wakamatsu, Fukushima, 965-8580, Japan2IMT RAS, Chernogolovka, 142432, Russia

Abstract Light-emitting diode (LED) with designed metalelectrode to the top p-semiconductor layer is studied. Originalnumerical model and procedure are developed for the LED withnonuniform distributions of electrical and optical characteristicscaused by the mesh-like configuration of the top electrode. Theproposed approach can be used to optimize the LED ouput opticalperformance by proper choice of the geometrical parameters ofthe meshed electrode.

I. INTRODUCTION

Output optical performance of the semiconductor light-emitting diodes (LEDs) with light extraction via top surface isadversely affected by the top metal electrode which preventsthe extraction of the light generated beneath it. A remarkableenhancement of optical output has been reported for blueGaN/InGaN LED with top metal electrode designed as a mesh[1]. Mechanism responsible for the enhancement of the lightextraction is related to the electric potential profile createdby the mesh-like electrode. At properly chosen geometricalparameters of the meshed electrode the potential may be strongenough to promote current injection and light generation in theactive region not only beneath the metal elements but in theuncovered portions as well [2]. The generated light is extractedvia the mesh windows. Fig. 1a shows the emission of the LEDthrough the windows in the mesh-like top p-electrode havinga horse-shoe shape, the central dark region is occupied by thesolid n-electrode. If the mesh pitch exceeds a certain valuethe light generation in the centers of the mesh windows maydisappear. Further pitch increase may cause the squeezing ofthe light-generating region to a configuration mimicking thatof the mesh.

To determine optimal geometrical parameters of the meshedcontact leading to the maximum optical output one needs toevaluate the output optical power of the LED. Such task isusually performed by numerical simulations based on MonteCarlo ray-tracing (MC RT) or finite-difference time domain(FDTD) techniques [3], [4]. In the case of the mesh-likeelectrode the distributions of electric potential, injected currentand intensity of generated light are spatially nonuniform alongthe active region which adds an extra complexity to thesimulation procedure.

This paper deals with a numerical analysis of the LED withtop metal electrode designed as a mesh. Numerical procedureis developed and used to simulate output optical performanceof the LED at different mesh parameters.

Fragment of the mesh window

(b) Mesh window

(c)

c

Active region

Active regionn-contact

Mesh-like p-electrode

xyz

a

SuSl

R

Fig. 1. (a) Emission of blue LED through the windows in the meshedtop electrode. (b) Schematic structure of the LED with solid bottom - anddesigned as a mesh top p-electrodes. (c) A fragment of the LED unit cellin a bi-plane representation. Lower and upper planes correspond to a light-generating layer and output semiconductor-air interface, respectively. NG-cellareas in two planes are different but related to each other.

II. MODELS. SIMULATION STRATEGY. RESULTS

A simplified model of an LED with narrow-gap activeregion sandwiched between top and bottom wide-gap p- andn-semiconductor layers schematically shown in Fig. 1b isconsidered. Top metal -electrode is designed as a mesh withpitch , the bottom -electrode is solid and grounded. Due toperiodicity of the mesh a unit cell (UC) of the LED structurebeneath a single mesh cell is considered. Computation domainof the UC is represented by a bi-plane model. Lower andupper planes correspond to a light-generating layer and outputsemiconductor-air interface, respectively. Areas of numericalgrid (NG) cells in the lower () and upper () planesare set to be related to each other: = cos3 , is the angle of total internal reflection at the semiconductor-

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air interface. Elementary volume of the light-generatinglayer corresponding to each NG-cell of area is treated as apoint light source emitting light isotropically. However, lightemitted in the lower hemisphere is assumed to be absorbedand is not taken into account.

The power of light generated in the elementary volume of the active region is related to the injected current and canbe expressed in the form [5]

=

0 exp

(

(, , )

), (1)

where and are the Plancks constant and frequency oflight; is internal quantum efficiency, and are electroncharge and the Boltzmann constant, is the temperature inKelvin, 0 is the saturation current per unit area, (, , )is potential in the plane of -heterojunction (lower plane), = , is the distance between upper and lowerplanes, is the thickness of the LED structure. Approximatingthe mesh elements by wires of radius we arrive at thefollowing expression for the potential:

(, , ) = 2 ln

cosh 2 ( ) cos 2 cosh 2 ( + ) cos 2

ln cosh2 ( ) cos 2

cosh 2 ( + ) cos 2 , (2)

where =1/(2 ln(/(2)) + 4/).

Light photons coming to the upper plane at the angles can be successfully extracted. To calculate the power oflight photons which can escape from each NG-cell in the upperplane we sum the contributions of all NG-cells within thecircle area (Fig. 1c) of radius = tan .

(, ) 42

0

,

() exp[

(, , )

]. (3)

Here () is transmission coefficient. Light photons comingfrom the NG-cells in the center of the circle and from its rimcover different portions of the of the area , as it is shownin Fig. 1c. To promote the complete collection of light bysimulation procedure we introduce function playing therole of angular-dependent aperture

=(cos cos

)3. (4)

The developed procedure was used to simulate spatial dis-tributions of output optical power at different geometricalparameters of the mesh. The distribution of output opticalpower along the mesh window is shown in Fig. 2a at meshpitch = 600 nm, 1 = 6.25 V, = 800 nm, = 200 nm, = 2.5. To find the total output power of the LED we need tosum the output power over all NG-cells in the window of oneUC and then multiply by the number of the UCs. Normalizedtotal output optical power versus mesh pitch shown in Fig. 2bfor different wire radii .

00.2

0.40.6

0.81

0

0.5

10

0.2

0.4

0.6

0.8

1

1.2

x 1011

Distance x/a. arb.

u.Distance

y/a, arb.u.

Nor

mal

ized

out

put o

ptica

l pow

er, a

rb.u

.

a = 600 nm

500 600 700 800 900Mesh pitch a, nm

0

0.5

1

1.5

2

Nor

mal

ized

tota

l out

put

optic

al p

ower

x10

-6 ,

ar

b.u.

r = 50 nm 75 nm

Fig. 2. (a) Spatial distributions of normalized output optical power alongmesh window at mesh pitches = 600 nm; (b) Total normalized outputoptical power versus mesh pitch at different width of the mesh elements.

III. CONCLUSIONSNumerical model and simulation strategy are developed to

evaluate optical output performance of the LED with the topmetal electrode patterned as a mesh. In the model the light-generating layer has been represented as a system of pointlight sources with isotropic emission. Bi-plane computationdomain has been introduced. NG-cell areas in the two planesof the computation domain are set to be related to eachother. Angle-tuned aperture function is introduced to adjustthe light collection by numerical procedure. The developedprocedure is used to simulate spatial distributions of outputoptical power along the mesh windows and total optical powerof the LED. The numerical model and procedure can be usedin optimization of the LED output optical performance.

REFERENCES[1] S. Shapoval, M. Barabanenkov, V. Sirotkin, E. Polushkin, L. Saptsova,

A. Kovalchuk, et al., High efficiency LED with optoelectronicallyoptimized p-contact Proc. of WOCSDICE 2007, Venice, Italy, p. 29,2007.

[2] A. Konishi, R. Yamase, I. Khmyrova, J. Kholopova, E. Polushkin, A.Kovalchuk, V. Sirotkin, and S. Shapoval, Analytical model of light-emitting diodes with patterned contact Opt. Rev., vol. 20, 214-2172013.

[3] V. Zabelin, D. A. Zakheim, and S. A. Gurevich, Efficiency im-provement of AlGaInN LEDs advanced by ray-tracing analysis, IEEEJ. Quant. Electron., vol. 40, 1675-1686, 2004.

[4] Y. Kawaguchi, K. Nishizono, J.-S. Lee, and H. Katsuda, Light extractionsimulation of surface- textured light-emitting diodes by finite-differencetime-domain method and ray-tracing method, Jpn. J. Appl. Phys., vol.46, 31-34, 2007.

[5] M. Fukuda, Optical Semiconductor Devices, New York: Wiley, 1999,p. 77-100.

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