江衍偉臺灣大學：光電工程學研究所陳廷仰Chen, Tyng-YangTyng-YangChen2007-11-252018-07-052007-11-252018-07-052004http://ntur.lib.ntu.edu.tw//handle/246246/50763本論文中，我們模擬分析了各種光子晶體平板微共振腔的輻射特性。由於光子晶體具有布拉格反射和全反射的效應，光可以侷限在缺陷中，這類光子晶體可用於製作發光二極體。吾人利用三維之有限時域差分法，分別針對方形晶格和三角形晶格缺陷結構的輻射特性進行模擬。吾人先探討缺陷附近空氣洞大小和輻射特性的關係，接著調整空氣洞的位置和形狀。在某些結構下，只需稍微適當的改變缺陷附近的結構，便可有效增進輻射效率，而不需大幅改變整體的結構或介質的折射率。最後我們歸納一些結論，以供設計高效能發光二極體參考。Abstract In this thesis, the radiation characteristics of various kinds of photonic crystal slab microcavites are numerically investigated. Light is confined within the defect region by the combined action of distributed Bragg reflection and total internal reflection. This kind of photonic crystal has been employed in making a semiconductor light-emitting diode (LED). By using the three-dimensional finite-difference time-domain (FDTD) method, we calculate the radiation characteristics for the square-lattice or triangular-lattice microcavity consisting of a single defect. The relation between the radiation characteristics and the radii of air holes around the defect is discussed. Then, the positions and shapes of nearest holes are adjusted. In some structures, we only need to perform small adjustment of the defect geometry to get better radiation characteristics, without significantly changing the photonic crystal structure and refractive index of dielectric material. Some conclusions are drawn, which may be helpful for designing efficient LEDs.Contents Contents Chapter 1 Introduction 1 1.1 Background 1 1.2 Semiconductor light-emitting diodes 2 1.3 Motivation of this study………………………………..4 Chapter 2 Theoretical Formulations 7 2.1 Problem geometry 7 2.1.1 Introduction…………………………………………7 2.1.2 Single-point defect in square lattice…………7 2.1.3 Single-point defect in triangular lattice……..10 2.2 Maxwell’s equations……………………………11 Chapter 3 Finite-Difference Time-Domain Method………………………….18 3.1 Introduction 18 3.2 Three-dimensional FDTD algorithms 19 3.3 Stability criterion and Mur’s absorbing boundary condition 23 3.4 Definitions of parameters………………………………….25 Chapter 4 Simulation Results 29 4.1 Square lattice………………………………………….29 4.1.1 Square-lattice point defect ………………………….29 4.1.2 Changing the radius rx near the defect…………………...32 4.1.3 Changing the positions of the nearest holes in the x-direction………………………………………..33 4.1.4 Changing the radius ry near the defect……………..……34 4.1.5 Changing the positions of the nearest holes in the y-direction...………………………………...……35 4.1.6 Elliptical holes in the x-direction near the defect…..........36 4.1.7 Elliptical holes in the y-direction near the defect…..........36 4.1.8 Discussions……………………………..............…37 4.2 Triangular lattice……………………….………...…………41 4.2.1 Triangular-lattice point defect…………………………...41 4.2.2 Changing the radius of rx near the defect……………….43 4.2.3 Changing the positions of the nearest holes in the x-direction………..………………………………44 4.2.4 Changing the radius of holes near the defect……………44 4.2.5 Elliptical holes in the x-direction near the defect…….....45 4.2.6 X-directed point dipole source in triangular lattice……...46 4.2.7 Discussions……………………………………..……….46 Chapter 5 Conclusions 86 References…………………………………………………..881709910 bytesapplication/pdfen-US光子晶體photonic crystalthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/50763/1/ntu-93-R91941030-1.pdf