光子晶體(photonic crystal)是由不同折射率材料排列而成的人造結構，具多種維度形式的周期性排列，經由適度的設計，可以有效控制電磁波的傳遞效果。一般而言，光子晶體具有多方面的應用，如波導、共振腔、反射器、光纖、發光二極體、太陽能電池等。發光二極體(light emitting diode)是透過摻雜的方式使半導體材料成為 p型與n型，再把它們接合在一起形成p-n接面。電子及電洞可以容易地從n型及p型的材料注入，而當電子與電洞相遇而結合，就會以光子的形式釋放出能量。

光子晶體用來讓發光二極體提升發光效率主要有兩種機制，一種是讓發光波長落在可輻射出光子晶體的輻射模態，當光打入光子晶體時，光線能從結構中萃取出來；另一種是讓發光波長落在二維光子晶體能隙內，當光進入光子晶體時，由於無法在二維光子晶體的平面方向傳導，使得光線往垂直方向透射出。

本文利用阿基米德晶格(Archimedean lattice)與傳統三角晶格做比較，藉由蝕刻氮化鎵空氣柱，變換共振腔中心的缺陷(H1、H2)，使用平面波展開法(PWEM)運算能隙，讓電磁波波段集中在共振腔中心，最後再置入發光二極體，利用時域有限差分法(FDTD)模擬 LED，提升發光效率。

Photonic crystals(PhCs) are artificial multi-dimension periodic structures with periodic modulation of the refractive index. Suitably designed, PhCs have the ability to control the propagation of light. Generally, PhCs have a wide range of applications, such as waveguides, resonant cavities, reflectors, optical fiber,light-emitting diodes (LED), solar cells.
Light-emitting diode is a p-type and n-type semiconductor material doped, by way of joining them together and then forming the p-n junction. Electrons and holes can be easily obtained from the n-type and p-type material is injected, and when the electrons and holes recombine within the device, releasing energy in the form of photons.

To enhancing the light extraction efficiency, the PhCs have both guide and radiation modes. The guide mode allows the lights to transmit internally. One is to allow the emission wavelength of the radiation fall out radiation mode photonic crystal, when light is into the photonic crystal, it is extracted from the structure.Another is to allow the emission wavelength falls within the two-dimensional photonic crystals bandgap crystals. When light is emitting, it unable conduct in the
plane of the two-dimensional photonic crystal, then making the light escape of vertical transmission.

In this paper, we use Archimedes lattice compared with the traditional triangular lattice, with air holes etched GaN, designated the defects , namely H1 and H2 are in the center of the cavities. By using the plane wave expansion method (PWEM) we design the structural parameter, so that electromagnetic waves concentrated in the center of the cavity. And then using the finite-difference time-domain (FDTD) method to simulate the LEE from the PhC-LED.

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