微纳米结构增强蓝光LED发光效率的研究
|
摘要
在世界范围处于能源危机的当今社会,LED作为一种新型的绿色光源,具有环保节能、可靠性高、使用寿命长等优点,在照明领域将引领未来发展的趋势,有望成为继白炽灯、荧光灯、高强度气体放电灯之后的“第四代光源”。世界各国政府已开始重视LED的研究和开发,争相提出各自的发展计划或出台一些扶持措施。
自LED问世以来,固体白光照明光源是人们一直努力追寻的目标。目前蓝光LED是制造白光LED的基础,蓝光LED主要是由GaN材料制成的,所以研究GaN基蓝光LED对发展白光LED有重要意义。LED的发光效率是衡量LED性能的重要指标,目前LED发光效率还存在很大的提升空间,特别是GaN基LED。由于GaN材料和空气之间大的折射率差异,使得大部分光在分界面处产生全内反射和菲涅尔反射而陷落在材料中。目前围绕如何提高GaN基LED光提取效率的问题开展了大量工作。多种方法已被提出来提高GaN基LED的光提取效率,如表面粗化、倒装芯片结构、光子晶体、图形化衬底技术、微纳米复合结构等。在制作微纳米结构增加LED发光效率的电磁场特性的研究中,LED样品的生长和微纳米结构的制作都是一个非常耗时、耗力和耗财的过程。为了节约光电器件制作成本,可以借助计算机技术来加快设计过程并且降低开发成本。
本论文围绕提高蓝光LED发光效率为目的,采用微纳米GaN图形结构,通过计算机模拟和理论分析相结合的方法研究了微纳米图形结构对蓝光LED光提取效率的影响。基本思路是采用数值仿真技术通过对蓝光LED结构建模,研究了微纳米图形结构的结构参数对蓝光LED光提取效率的影响,通过对结构参数进行优化,并结合理论分析,最终获得具有高提取效率的LED优化结构,为实现高效蓝光LED提供理论指导。
本论文开展的主要研究工作有以下几点：
(1)分析并研究了FDTD算法和蒙特卡洛射线追踪法在进行LED光提取效率计算时的适用性。FDTD算法以将麦克斯韦旋度方程直接在时域-空域进行差分离散,通过逐步推进的方法求解空间电磁场。针对具有纳米图形结构的LED数值仿真是非常有效的。蒙特卡洛射线追踪法是依据光在均匀媒质中的直线传播定律以及光在两种不同媒质界面上的反射和折射定律为基础,把光看作为光能量传播方向上的几何线。运用此方法很容易模拟LED有源层电子-空穴对的自发辐射过程,并且适用于任何形状和尺度的结构。这种方法对具有微米量级图型结构的LED仿真是可行并可靠的。
(2)通过数值建模,运用FDTD算法计算了光子晶体LED,特别是嵌入式光子晶体对LED的光提取效率的影响。重点研究了嵌入式光子晶体结构参数(如填充因子、位置、厚度)对蓝光LED光提取效率的影响,同时与表面光子晶体对LED光提取效率的影响进行了比较。结果表明嵌入式光子晶体的填充因子和位置对光提取效率影响较大,而厚度对其影响较小。光子晶体厚度对LED光提取效率的影响呈现一种震荡状态。在表面光子晶体深度刻蚀(深度250nm)时可使光提取效率有5倍以上的增加。表面光子晶体和嵌入式光子晶体在对LED进行光提取上起的作用不同。顶端光子晶体主要是通过对导模的衍射作用增加光提取效率,而嵌入式光子晶体主要贡献是改变LED中导模的分布。通过对嵌入式光子晶体结构参数的优化,更进一步通过双光晶体增加LED光提取效率提供了理论指导。
(3)在光子晶体的制作过程中,不可避免的会出现结构上的缺陷和无序,而这些缺陷或无序会严重影响光子晶体的性能。本文通过程序设计产生了具有一定容差的光子晶体,即无序光子晶体。结合FDTD方法通过数值建模得到具有无序光子晶体结构的LED模型。同时研究了无序光子晶体LED有源层位置对光提取的影响。研究发现,无序结构的出现并未改变有源层位置随光提取效率的影响,与平板结构相同。
(4)为了进一步得到光子晶体结构参数的无序变化对蓝光LED光提取效率的影响,分别选取了具有优化结构参数的光子晶体和非优化结构参数的光子晶体进行研究对比。主要研究了光子晶体空气孔位置、半径和刻蚀深度的无序变化对蓝光LED光提取效率的影响。研究表明,空气孔位置的无序变化一般呈现弱无序状态,对光提取效率的影响不显著；空气孔半径的无序变化可以显著的影响蓝光LED的光提取效率,最大变化幅度可达54%;空气孔在深度刻蚀情况下,刻蚀深度在20%的容差变化范围内,对光提取效率的影响可以忽略。对于优化的光子晶体结构,任何的无序变化都会使光提取效率下降,而对于非优化的光子晶体结构,结构参数的无序变化反而会使光提取效率增加。这部分研究结果说明不同结构参数的光子晶体LED受结构参数无序变化的影响不同,但每个光子晶体LED会存在一组优化参数,使光提取效率达到最大,其它光子晶体结构参数的无序变化,都会使光提取效率减小。
(5)在LED表面制作微表面结构,一是可以增加光的散射,二是会起到一定抗反射的作用。利用蒙特卡洛射线追踪法研究了各种不同的周期图形阵列对蓝光倒装LED光提取效率的影响。并结合表面抗反射理论和等效折射率理论对数值研究结果给出了详尽的理论分析。结果表明,在四种不同的周期阵列中,微锥阵列可以提供最好的光提取效率,锥阵列结构要优于柱阵列结构,凸起结构要优于孔状结构。为了找到利于光提取效率增加的优化微结构,比较了微锥阵列结构和微金字塔阵列结构对光提取效率的影响。结果表明,在具有相同的图形底面积和倾斜角的情况下,微锥阵列优于微金字塔阵列。考虑到实际的图形结构制作工艺,严格的锥结构很难获得,研究了截断的锥或锥孔阵列顶半径对光提取效率的影响。研究表明具有一定顶半径的截断的锥或锥孔阵列反而更有利于光提取效率的增加。
In order to handle the energy crisis around the world, LED as a new green light source has the advantages, such an environmental protection and energy saving, high reliability, long-time life, which will lead the future trend of development in the lighting field. It is expected to become the fourth generation light source after incandescent lamp, fluorescent lamp, high intensity discharge lamp. Many governments have begun to attach importance to the research and development of LED and proposed development plan or some measures to support it.
Since the LED was inverted, solid state lighting is a pursued goal. The blue LED is the basis for manufacturing white LED and is mainly made of GaN material, so it has important significance to study the GaN-based blue LED for the development of white LED. The luminous efficiency of the LED is an important parameter to decide the performance of the LED. There is still much room for improving the luminous efficiency, especially the GaN-based LED. Because the refractive index difference is large between the GaN material and air, most of light are collapsed into GaN materials by the total internal reflection and the Fresnel reflection. At present, a lot of work has been carried out about how to improve the light extraction efficiency of GaN-based LED. Many research teams has employed a variety of methods to improve the light extraction efficiency of GaN-based LED, such as surface roughening,, flip-chip structure, photonic crystals, patterned sapphire substrate technology, micro/nano hybrid structures etal. The growth of LED and the fabrication of the micro/nano structures are a very time-consuming, labor-consuming and cost-consuming process. In order to save the fabrication cost of the optoelectronic device, computer technology can be used to speed up the design process and reduce the cost of development.
In this paper, we focused on enhancing the blue LED light emitting efficiency as the goal and used the micro/nano patterned structure as research way through the combination of computer simulation and theoretical analysis. The GaN-based LED models were established by computer simulation technology and the effects of micro/nano patterned structural parameters on the light extraction efficiency were studied and the optimized structure parameters were obtained by optimizing the structure, thus the results can provide a theoretical basis for high efficient GaN-based LED.
In this paper, the main works are as follows:
(1) The FDTD algorithm and Monte Carlo ray-tracing method were used to calculate the light extraction efficiency for different patterned structure. The FDTD algorithm is that the Maxwell equations are directly separated in time-space through thestep-by-step method. The method is very effective for the numerical simulation of LED with nano-patterned structure. Monte Carlo ray-tracing method is based on geometric optics. Propagation of light obeys the law of reflection and refraction on the interface of two different media.It is easy for this method to simulate spontaneous emission process of electron-hole pairs in active layer, it is applicable to the structures of any shape and size. The results are feasible and reliable for the LED with the micro-patterned structure
(2) Through numerical simulation, the extraction efficiency of photonic crystal LED was calculated by using FDTD algorithm. The work focused on the effects of the embedded photonic crystal structure parameters (such as the fill factor, location, thickness) on light extraction efficiency of blue LED LED, compared with the effects of surface photonic crystals.The results showed that the filling factor and the position of embedded photonic crystals had larger effects on the light extraction efficiency, and the thickness had little influence. Effects of the thickness of photonic crystal on the light extraction efficiency appeared up and down. The etched depth (depth250nm) of surface photonic crystal can make the increment of the light extraction efficiency more than5times. Surface Photonic crystal and embedded photonic crystal surface played different role for light extraction. The surface photonic crystal mainly through the diffraction effect of guided mode to increase the light extraction efficiency, and the embedded photonic crystal is to change the distribution of guided modes in LED. Through the optimization of the structure parameters of embedded photonic crystal, further by double crystal LED it can provide theoretical guidance for increasing the light extraction efficiency by double photonic crystals.
(3)During the fabrication of photonic crystals, there will inevitably be structural defect and disorder, and the defect or disorder will affect the performance of photonic crystals. In this paper, the photonic crystals with a certain tolerance were produced by computer programming, namely the disordered photonic crystals. The LED with disordered photonic crystals is obtained by combining with the FDTD method. The effect of the position of active layer in the LED with disordered photonic crystal LED was studied on the light extraction efficiency. The results showed that disordered structure didn't change the effect, compared with conventional LED.
(4) In the fabrication process of the photonic crystals, the disorder and the defect can affect seriously the properties of photonic crystals. In order to further get the effects of the disordered photonic crystal structural parameters on the light extraction efficiency of blue LED, photonic crystals with optimized structural parameters and with non-optimized structural parameters were selected. The effect of disordered change of photonic crystals is studied on the blue LED light extraction efficiency, such as air hole, the radius, and etched depth. The results showed that the disordered change of hole position was a weak disordered state and had no significant effect on the light extraction efficiency; disordered change of the radius of air hole can significantly influence the extraction efficiency of blue LED and the largest54%increment of the extraction efficiency could be obtained; For the deep-etched air holes, the etched depth change in the tolerance range of20%change can be ignored on the effect of light extraction efficiency. For the optimized photonic crystals, any disordered change will make the light extraction efficiency decreased. However, for non-optimized photonic crystals, disordered change of structural parameters can make the light extraction efficiency increased. These results showed that photonic crystal LEDs with the different structural parameters can lead to different effects due to the disordered change of structural parameters. But for each photonic crystal LED, there will be a set of optimization parameters to make the light extraction efficiency maximized, and disordered change of other photonic crystal parameters will cause the light extraction efficiency decreased.
(5) Surface micro-structures used in LED can play an important role for light scattering and anti-reflection. The effects of periodic arrays on the extraction efficiency of the flip-chip LED were studied by Monte Carlo ray tracing method. The detailed theoretical analysis was given by the surface anti-reflection theory and the effective refractive index theory. The results showed that micro-cone arrays could provide the best light extraction efficiency in the four different periodic arrays. The cone arrays were better than pillar arrays and convex structure was better than well structure for light extraction. Furthermore, micro-cone arrays and the micro-pyramid structures were compared. The results showed that micro-cone arrays were better than micro-pyramid arrays at the same base area and the inclined angle. Considering the fabrication processes of actual cone arrays, the effects of the top radius were studied on light extraction efficiency of the truncated cone or cone well arrays. The results showed that the LEDs with cone or cone-hole arrays of certain top radius were preferable for light extraction.
自LED问世以来,固体白光照明光源是人们一直努力追寻的目标。目前蓝光LED是制造白光LED的基础,蓝光LED主要是由GaN材料制成的,所以研究GaN基蓝光LED对发展白光LED有重要意义。LED的发光效率是衡量LED性能的重要指标,目前LED发光效率还存在很大的提升空间,特别是GaN基LED。由于GaN材料和空气之间大的折射率差异,使得大部分光在分界面处产生全内反射和菲涅尔反射而陷落在材料中。目前围绕如何提高GaN基LED光提取效率的问题开展了大量工作。多种方法已被提出来提高GaN基LED的光提取效率,如表面粗化、倒装芯片结构、光子晶体、图形化衬底技术、微纳米复合结构等。在制作微纳米结构增加LED发光效率的电磁场特性的研究中,LED样品的生长和微纳米结构的制作都是一个非常耗时、耗力和耗财的过程。为了节约光电器件制作成本,可以借助计算机技术来加快设计过程并且降低开发成本。
本论文围绕提高蓝光LED发光效率为目的,采用微纳米GaN图形结构,通过计算机模拟和理论分析相结合的方法研究了微纳米图形结构对蓝光LED光提取效率的影响。基本思路是采用数值仿真技术通过对蓝光LED结构建模,研究了微纳米图形结构的结构参数对蓝光LED光提取效率的影响,通过对结构参数进行优化,并结合理论分析,最终获得具有高提取效率的LED优化结构,为实现高效蓝光LED提供理论指导。
本论文开展的主要研究工作有以下几点：
(1)分析并研究了FDTD算法和蒙特卡洛射线追踪法在进行LED光提取效率计算时的适用性。FDTD算法以将麦克斯韦旋度方程直接在时域-空域进行差分离散,通过逐步推进的方法求解空间电磁场。针对具有纳米图形结构的LED数值仿真是非常有效的。蒙特卡洛射线追踪法是依据光在均匀媒质中的直线传播定律以及光在两种不同媒质界面上的反射和折射定律为基础,把光看作为光能量传播方向上的几何线。运用此方法很容易模拟LED有源层电子-空穴对的自发辐射过程,并且适用于任何形状和尺度的结构。这种方法对具有微米量级图型结构的LED仿真是可行并可靠的。
(2)通过数值建模,运用FDTD算法计算了光子晶体LED,特别是嵌入式光子晶体对LED的光提取效率的影响。重点研究了嵌入式光子晶体结构参数(如填充因子、位置、厚度)对蓝光LED光提取效率的影响,同时与表面光子晶体对LED光提取效率的影响进行了比较。结果表明嵌入式光子晶体的填充因子和位置对光提取效率影响较大,而厚度对其影响较小。光子晶体厚度对LED光提取效率的影响呈现一种震荡状态。在表面光子晶体深度刻蚀(深度250nm)时可使光提取效率有5倍以上的增加。表面光子晶体和嵌入式光子晶体在对LED进行光提取上起的作用不同。顶端光子晶体主要是通过对导模的衍射作用增加光提取效率,而嵌入式光子晶体主要贡献是改变LED中导模的分布。通过对嵌入式光子晶体结构参数的优化,更进一步通过双光晶体增加LED光提取效率提供了理论指导。
(3)在光子晶体的制作过程中,不可避免的会出现结构上的缺陷和无序,而这些缺陷或无序会严重影响光子晶体的性能。本文通过程序设计产生了具有一定容差的光子晶体,即无序光子晶体。结合FDTD方法通过数值建模得到具有无序光子晶体结构的LED模型。同时研究了无序光子晶体LED有源层位置对光提取的影响。研究发现,无序结构的出现并未改变有源层位置随光提取效率的影响,与平板结构相同。
(4)为了进一步得到光子晶体结构参数的无序变化对蓝光LED光提取效率的影响,分别选取了具有优化结构参数的光子晶体和非优化结构参数的光子晶体进行研究对比。主要研究了光子晶体空气孔位置、半径和刻蚀深度的无序变化对蓝光LED光提取效率的影响。研究表明,空气孔位置的无序变化一般呈现弱无序状态,对光提取效率的影响不显著；空气孔半径的无序变化可以显著的影响蓝光LED的光提取效率,最大变化幅度可达54%;空气孔在深度刻蚀情况下,刻蚀深度在20%的容差变化范围内,对光提取效率的影响可以忽略。对于优化的光子晶体结构,任何的无序变化都会使光提取效率下降,而对于非优化的光子晶体结构,结构参数的无序变化反而会使光提取效率增加。这部分研究结果说明不同结构参数的光子晶体LED受结构参数无序变化的影响不同,但每个光子晶体LED会存在一组优化参数,使光提取效率达到最大,其它光子晶体结构参数的无序变化,都会使光提取效率减小。
(5)在LED表面制作微表面结构,一是可以增加光的散射,二是会起到一定抗反射的作用。利用蒙特卡洛射线追踪法研究了各种不同的周期图形阵列对蓝光倒装LED光提取效率的影响。并结合表面抗反射理论和等效折射率理论对数值研究结果给出了详尽的理论分析。结果表明,在四种不同的周期阵列中,微锥阵列可以提供最好的光提取效率,锥阵列结构要优于柱阵列结构,凸起结构要优于孔状结构。为了找到利于光提取效率增加的优化微结构,比较了微锥阵列结构和微金字塔阵列结构对光提取效率的影响。结果表明,在具有相同的图形底面积和倾斜角的情况下,微锥阵列优于微金字塔阵列。考虑到实际的图形结构制作工艺,严格的锥结构很难获得,研究了截断的锥或锥孔阵列顶半径对光提取效率的影响。研究表明具有一定顶半径的截断的锥或锥孔阵列反而更有利于光提取效率的增加。
In order to handle the energy crisis around the world, LED as a new green light source has the advantages, such an environmental protection and energy saving, high reliability, long-time life, which will lead the future trend of development in the lighting field. It is expected to become the fourth generation light source after incandescent lamp, fluorescent lamp, high intensity discharge lamp. Many governments have begun to attach importance to the research and development of LED and proposed development plan or some measures to support it.
Since the LED was inverted, solid state lighting is a pursued goal. The blue LED is the basis for manufacturing white LED and is mainly made of GaN material, so it has important significance to study the GaN-based blue LED for the development of white LED. The luminous efficiency of the LED is an important parameter to decide the performance of the LED. There is still much room for improving the luminous efficiency, especially the GaN-based LED. Because the refractive index difference is large between the GaN material and air, most of light are collapsed into GaN materials by the total internal reflection and the Fresnel reflection. At present, a lot of work has been carried out about how to improve the light extraction efficiency of GaN-based LED. Many research teams has employed a variety of methods to improve the light extraction efficiency of GaN-based LED, such as surface roughening,, flip-chip structure, photonic crystals, patterned sapphire substrate technology, micro/nano hybrid structures etal. The growth of LED and the fabrication of the micro/nano structures are a very time-consuming, labor-consuming and cost-consuming process. In order to save the fabrication cost of the optoelectronic device, computer technology can be used to speed up the design process and reduce the cost of development.
In this paper, we focused on enhancing the blue LED light emitting efficiency as the goal and used the micro/nano patterned structure as research way through the combination of computer simulation and theoretical analysis. The GaN-based LED models were established by computer simulation technology and the effects of micro/nano patterned structural parameters on the light extraction efficiency were studied and the optimized structure parameters were obtained by optimizing the structure, thus the results can provide a theoretical basis for high efficient GaN-based LED.
In this paper, the main works are as follows:
(1) The FDTD algorithm and Monte Carlo ray-tracing method were used to calculate the light extraction efficiency for different patterned structure. The FDTD algorithm is that the Maxwell equations are directly separated in time-space through thestep-by-step method. The method is very effective for the numerical simulation of LED with nano-patterned structure. Monte Carlo ray-tracing method is based on geometric optics. Propagation of light obeys the law of reflection and refraction on the interface of two different media.It is easy for this method to simulate spontaneous emission process of electron-hole pairs in active layer, it is applicable to the structures of any shape and size. The results are feasible and reliable for the LED with the micro-patterned structure
(2) Through numerical simulation, the extraction efficiency of photonic crystal LED was calculated by using FDTD algorithm. The work focused on the effects of the embedded photonic crystal structure parameters (such as the fill factor, location, thickness) on light extraction efficiency of blue LED LED, compared with the effects of surface photonic crystals.The results showed that the filling factor and the position of embedded photonic crystals had larger effects on the light extraction efficiency, and the thickness had little influence. Effects of the thickness of photonic crystal on the light extraction efficiency appeared up and down. The etched depth (depth250nm) of surface photonic crystal can make the increment of the light extraction efficiency more than5times. Surface Photonic crystal and embedded photonic crystal surface played different role for light extraction. The surface photonic crystal mainly through the diffraction effect of guided mode to increase the light extraction efficiency, and the embedded photonic crystal is to change the distribution of guided modes in LED. Through the optimization of the structure parameters of embedded photonic crystal, further by double crystal LED it can provide theoretical guidance for increasing the light extraction efficiency by double photonic crystals.
(3)During the fabrication of photonic crystals, there will inevitably be structural defect and disorder, and the defect or disorder will affect the performance of photonic crystals. In this paper, the photonic crystals with a certain tolerance were produced by computer programming, namely the disordered photonic crystals. The LED with disordered photonic crystals is obtained by combining with the FDTD method. The effect of the position of active layer in the LED with disordered photonic crystal LED was studied on the light extraction efficiency. The results showed that disordered structure didn't change the effect, compared with conventional LED.
(4) In the fabrication process of the photonic crystals, the disorder and the defect can affect seriously the properties of photonic crystals. In order to further get the effects of the disordered photonic crystal structural parameters on the light extraction efficiency of blue LED, photonic crystals with optimized structural parameters and with non-optimized structural parameters were selected. The effect of disordered change of photonic crystals is studied on the blue LED light extraction efficiency, such as air hole, the radius, and etched depth. The results showed that the disordered change of hole position was a weak disordered state and had no significant effect on the light extraction efficiency; disordered change of the radius of air hole can significantly influence the extraction efficiency of blue LED and the largest54%increment of the extraction efficiency could be obtained; For the deep-etched air holes, the etched depth change in the tolerance range of20%change can be ignored on the effect of light extraction efficiency. For the optimized photonic crystals, any disordered change will make the light extraction efficiency decreased. However, for non-optimized photonic crystals, disordered change of structural parameters can make the light extraction efficiency increased. These results showed that photonic crystal LEDs with the different structural parameters can lead to different effects due to the disordered change of structural parameters. But for each photonic crystal LED, there will be a set of optimization parameters to make the light extraction efficiency maximized, and disordered change of other photonic crystal parameters will cause the light extraction efficiency decreased.
(5) Surface micro-structures used in LED can play an important role for light scattering and anti-reflection. The effects of periodic arrays on the extraction efficiency of the flip-chip LED were studied by Monte Carlo ray tracing method. The detailed theoretical analysis was given by the surface anti-reflection theory and the effective refractive index theory. The results showed that micro-cone arrays could provide the best light extraction efficiency in the four different periodic arrays. The cone arrays were better than pillar arrays and convex structure was better than well structure for light extraction. Furthermore, micro-cone arrays and the micro-pyramid structures were compared. The results showed that micro-cone arrays were better than micro-pyramid arrays at the same base area and the inclined angle. Considering the fabrication processes of actual cone arrays, the effects of the top radius were studied on light extraction efficiency of the truncated cone or cone well arrays. The results showed that the LEDs with cone or cone-hole arrays of certain top radius were preferable for light extraction.
引文
[1]周志敏.LED照明与工程设计.北京：人民邮电出版社,2010.
[2]E. F. Schubert and J. K. Kim, "Solid-state light sources getting smart," Science, vol.308, pp. 1274-1278,2005.
[3]S. Nakamura, et al, "High-power GaN pn junction blue-light-emitting diodes," Japanese Journal of Applied Physics, vol.30, pp. L1998-L2001,1991.
[4]史光国.半导体发光二极管及固体照明.北京：科学出版社,2007.
[5]J. Kovac, et al., "Advanced light emitting diodes structures for optoelectronic applications," Thin solid films, vol.433, pp.22-26,2003.
[6]M. G. Craford, "LEDs for solid state lighting and other emerging applications:status, trends, and challenges," in Optics & Photonics 2005,2005, pp.594101-594101-10.
[7]H. J. Round, "A note on carborundum," Electrical world, vol.49, p.309,1907.
[8]B. Gudden and R. Pohl, "Das Quantenaquivalent bei der lichtelektrischen Leitung," Zeitschrift fur Physik A Hadrons and Nuclei, vol.17, pp.331-346,1923.
[9]H. Rupprecht, et al., "EFFICIENT VISIBLE ELECTROLUMINESCENCE AT 300°K FROM Ga 1-xAlxAs p-n JUNCTIONS GROWN BY LIQUID-PHASE EPITAXY," Applied Physics Letters, vol.11, pp.81-83,1967.
[10]H. Rupprecht, et al., "Efficient electroluminescence from GaAs diodes at 300 K," Applied Physics Letters, vol.9, pp.221-223,1966.
[11]N. Holonyak and S. Bevacqua, "Coherent (visible) light emission from Ga (Asl-xPx) junctions," Applied Physics Letters, vol.1, pp.82-83,1962.
[12]M. G. Craford and W. Groves, "Vapor phase epitaxial materials for LED applications," Proceedings of the IEEE, vol.61, pp.862-880,1973.
[13]E. F. Schubert, et al, Light emitting diodes:Wiley Online Library,2005.
[14]S. Nakamura, et al, "High-brightness InGaN/AlGaN double-heterostructure blue-green-light-emitting diodes," Journal of Applied Physics, vol.76, pp.8189-8191, 1994.
[15]S. Nakamura, et al, "Method of manufacturing p-type compound semiconductor," ed: Google Patents,1994.
[1]方志烈.半导体发光材料和器件.上海：复旦大学出版社,1992.
[2]A. David, "High-efficiency GaN-based light-emitting diodes:Light extraction by photonic crystals and microcavities," Ph. D. thesis, Ecole Polytechnique, Palaiseau, France,2006.
[3]周志敏.LED照明与工程设计.北京：人民邮电出版社,2010.
[4]K. Ramaiah, et al., "Characterization of InGaN/GaN multi-quantum-well blue-light-emitting diodes grown by metal organic chemical vapor deposition," Applied Physics Letters, vol.84, pp.3307-3309,2004.
[5]M. R. Krames, et al., "Status and future of high-power light-emitting diodes for solid-state lighting," Display Technology, Journal of, vol.3, pp.160-175,2007.
[6]A. I. Zhmakin, "Enhancement of light extraction from light emitting diodes," Physics Reports, vol.498, pp.189-241,2011.
[7]H. Amano, et al., "P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI)," Jpn. J. Appl. Phys, vol.28, pp. L2112-L2114,1989.
[8]S. Nakamura, et al., "Method of manufacturing p-type compound semiconductor," ed: Google Patents,1994.
[9]C. Wiesmann, "Nano-structured LEDs-Light extraction mechanisms and applications," 2010.
[10]S. P. DenBaars, et al, "Gallium nitride based light emitting diodes (LEDs) for energy efficient lighting and displays," in Electronics, Communications and Photonics Conference (SIECPC),2013 Saudi International,2013, pp.1-13.
[11]E. F. Schubert, et al, Light emitting diodes:Wiley Online Library,2005.
[12]M. G. Craford, "LEDs for solid state lighting and other emerging applications:status, trends, and challenges," in Optics& Photonics 2005,2005, pp.594101-594101-10.
[13]C.-F. Chu, et al, "High brightness GaN vertical light-emitting diodes on metal alloy for general lighting application," Proceedings of the IEEE, vol.98, pp.1197-1207,2010.
[14]O. Shchekin, et al, "High performance thin-film flip-chip InGaN-GaN light-emitting diodes" Applied Physics Letters, vol.89, pp.071109-071109-3,2006.
[15]S. Fan, et al, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Physical Review Letters, vol.78, p.3294,1997.
[16]R. K. Lee, et al, "Modified spontaneous emission from a two-dimensional photonic bandgap crystal slab," JOSA B, vol.17, pp.1438-1442,2000.
[17]马锡英.光子晶体原理及应用.北京：科学出版社,2010.
[18]Y. C. Shin, et al, "Effects of nanometer-scale photonic crystal structures on the light extraction from GaN light-emitting diodes," Quantum Electronics, IEEE Journal of, vol.46, pp.1375-1380,2010.
[19]K. McGroddy, et al, "Directional emission control and increased light extraction in GaN photonic crystal light emitting diodes," Applied Physics Letters, vol.93, pp. 103502-103502-3,2008.
[20]Y.-J. Lee, et al., "High light-extraction GaN-based vertical LEDs with double diffuse surfaces," Quantum Electronics, IEEE Journal of, vol.42, pp.1196-1201,2006.
[21]C.-C. Wang, et al., "Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure," Applied Physics Letters, vol.91, pp. 121109-121109-3,2007.
[22]江洋等.柱状与孔状图形衬底对MOVPE生长GaN体材料及LED器件的影响.物理学报vol.58,pp.3468-3473,2009.
[23]H. Gao, et al., "Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro-and nanoscale," Journal of Applied Physics, vol.103, pp.014314-014314-5,2008.
[24]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[25]C.-H. Chao, et al, "Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals," Applied Physics Letters, vol.89, pp.091116-091116-3,2006.
[26]H. Kim, et al, "Light-extraction enhancement of vertical-injection GaN-based light-emitting diodes fabricated with highly integrated surface textures," Optics letters, vol. 33, pp.1273-1275,2008.
[27]S. H. Kim, et al, "An improvement of light extraction efficiency for GaN-based light emitting diodes by selective etched nanorods in periodic microholes," Optics express, vol. 21, pp.7125-7130,2013.
[28]B. Sun, et al, "Light extraction enhancement of bulk GaN light-emitting diode with hemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[29]Y. Wang, et al, "On the Radiation Profiles and Light Extraction of Vertical LEDs with Hybrid Nanorod and Truncated Microdome Surface Textures," 2013.
[30]W. Lee, et al, "Enhanced light output of GaN-based vertical light-emitting diodes with superimposed circular protrusions and hexagonal cones," Electrochemical and Solid-State Letters, vol.14, pp. H53-H56,2011.
[1]葛德彪,闫玉波.电磁波时域有限差分方法西安：西安电子科技大学出版社,2005.
[2]M. Moharam and T. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," JOSA, vol.71, pp.811-818,1981.
[3]N. Chateau and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," JOSA A, vol.11, pp.1321-1331,1994.
[4]M. Moharam, et al., "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings:enhanced transmittance matrix approach," JOSA A, vol.12, pp. 1077-1086,1995.
[5]刘军.科学计算中的蒙特卡洛策略.北京：高等教育出版社,2009.
[6]劳彩莲,”基于蒙特卡洛光线跟踪方法的植物三维冠层辐射传输模型[D],”北京：中国农业大学博士论文,2005.
[7]P. Johns, "Application of the transmission-line-matrix method to homogeneous waveguides of arbitrary cross-section," Electrical Engineers, Proceedings of the Institution of, vol.119, pp.1086-1091,1972.
[8]W. J. Hoefer, "The transmission-line matrix method--theory and applications," Microwave Theory and Techniques, IEEE Transactions on, vol.33, pp.882-893,1985.
[9]K. J. Bathe, "Finite element method," Wiley Encyclopedia of Computer Science and Engineering,2008.
[10]G. Dhatt and G. Touzot, Finite Element Method:John Wiley & Sons,2012.
[11]K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," Antennas and Propagation, IEEE Transactions on, vol.14, pp. 302-307,1966.
[12]A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," Microwave Theory and Techniques, IEEE Transactions on, vol.23, pp.623-630,1975.
[13]G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," Electromagnetic Compatibility, IEEE Transactions on, pp.377-382,1981.
[14]J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," Journal of computational physics, vol.114, pp.185-200,1994.
[15]J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," Journal ofcomputational physics, vol.127, pp.363-379,1996.
[16]J. A. Roden and S. D. Gedney, "Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique," Microwave and Optical Technology Letters, vol.14, pp.71-75,1997.
[17]J. A. Roden and S. D. Gedney, "Convolutional PML (CPML):An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave and Optical Technology Letters, vol.27, pp.334-338,2000.
[18]R. Courant and D. Hilbert, Methods of mathematical physics vol.1:Wiley, com,2008.
[19]G. L. L. Buffon and F. N. Egerton, Selections from Natural history general and particular vol.2:Arno Press New York,1977.
[20]雷桂媛,“关于蒙特卡洛及拟蒙特卡洛方法的若干研究[D],”浙江:浙江大学博士学位论文,2003.
[21]牟旷凝,“蒙特卡洛方法和拟蒙特卡洛方法在期权定价中应用的比较研究,”科学技术与工程pp.1925-1928,2010.
[22]Y.-K. Ee, et al., "Light extraction efficiency enhancement of InGaN quantum wells light-emitting diodes with polydimethylsiloxane concave microstructures," Opt. Express, vol.17, pp.13747-13757,2009.
[1]E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Physical Review Letters, vol.58, p.2059,1987.
[2]S. John, "Strong localization of photons in certain disordered dielectric superlattices," Physical Review Letters, vol.58, pp.2486-2489,1987.
[3]V. Berger, et al, "Fabrication of a 2D photonic bandgap by a holographic method," Electronics Letters, vol.33, pp.425-426,1997.
[4]D.-H. Kim, et al, "Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns," Applied Physics Letters, vol.87, pp.203508-203508-3,2005.
[5]C. Wiesmann, "Nano-structured LEDs-Light extraction mechanisms and applications," 2010.
[6]C. Wiesmann, et al., "Photonic crystal LEDs-designing light extraction," Laser & Photonics Reviews, vol.3, pp.262-286,2009.
[7]L. Hong-Wei, et al., "Light extraction enhancement of GaN LED with a two-dimensional photonic crystal slab," Chinese Physics Letters, vol.28, p.054216,2011.
[8]A. David, et al., "Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution," Applied Physics Letters, vol.88, pp.061124-061124-3,2006.
[9]J. J. Wierer, et al., "Ⅲ-nitride photonic-crystal light-emitting diodes with high extraction efficiency," Nature Photonics, vol.3, pp.163-169,2009.
[10]E. Matioli and C. Weisbuch, "Impact of photonic crystals on LED light extraction efficiency: approaches and limits to vertical structure designs," Journal of Physics D:Applied Physics, vol.43, p.354005,2010.
[11]H. Kitagawa, et al, "Green GaInN photonic-crystal light-emitting diodes with small surface recombination effect," Applied Physics Letters, vol.98, pp.181104-181104-3,2011.
[12]Y.-W. Cheng, et al., "GaN-based LEDs surrounded with a two-dimensional nanohole photonic crystal structure for effective laterally guided mode coupling," Optics letters, vol. 36, pp.1611-1613,2011.
[13]马春生,刘式墉,光波导模式理论：吉林：吉林大学出版社,2007.
[14]A. Yariv and P. Yeh, Photonics:Optical Electronics in Modern Communications (The Oxford Series in Electrical and Computer Engineering):Oxford University Press, Inc., 2006.
[15]C. Xiong, et al, "Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals," Optics express, vol.17, pp.23684-23689,2009.
[16]B. Sun, et al., "Light extraction enhancement of bulk GaN light-emitting diode withhemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[17]H.-Y. Ryu, et al., "Enhancement of light extraction from two-dimensional photonic crystal slab structures," Selected Topics in Quantum Electronics, IEEE Journal of, vol.8, pp. 231-237,2002
[18]H. Gao, et al., "Improving light extraction efficiency of GaN-based LEDs by AlxGal-xN confining layer and embedded photonic crystals," 2012.
[19]杜刘革,“基于多GPU的FDTD并行算法及其在电磁仿真中的应用[D],”山东大学博士学位论文,2011.
[20]A. David, "High-efficiency GaN-based light-emitting diodes:Light extraction by photonic crystals and microcavities," Ph. D. thesis, Ecole Polytechnique, Palaiseau, France,2006.
[21]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[22]高晖等.双层光子晶体氮化镓蓝光发光二极管结构优化的研究.物理学报,vol.61, pp. 127807-127807,2012.
[1]许兴胜,陈弘达等.非晶光子晶体中的光子局域化.物理学报vol.55,pp.6430-6434,2006.
[2]K.-C. Kwan, et al, "Effects due to disorder on photonic crystal-based waveguides," Applied Physics Letters, vol.82, pp.4414-4416,2003.
[3]S. Mazoyer, et al., "Disorder-induced multiple scattering in photonic-crystal waveguides," Physical Review Letters, vol.103, p.063903,2009.
[4]H. De Raedt, et al, "Transverse localization of light," Physical Review Letters, vol.62, pp. 47-50,1989.
[5]Y. A. Vlasov, et al., "Different regimes of light localization in a disordered photonic crystal," Physical Review B, vol.60, p.1555,1999.
[6]朱志宏等.光子晶体的非严格周期性对其传输特性的影响.光学学报,vol.24, pp. 847-850,2004.
[7]D. H. Long, et al., "Analysis of disordered photonic crystal implemented in light-emitting diode for high light extraction efficiency," Japanese Journal of Applied Physics, vol.47, p. 4527.2008.
[8]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[9]陈健等.光子晶体结构参数的随机扰动对光子晶LED出光效率的研究.光学学报,pp.233-236,2010.
[10]B. Wang, et al., "Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,"Journal of Applied Physics, vol.106, pp.014508-014508-5,2009.
[11]L. Yan," Influence of Disordered Photonic Crystal on Light Extraction of a Kind of Light-emitting Diode Model," Acta Photonica Sinica, vol.6,2006.
[12]岳庆炀等.基于缺陷光子晶体结构的GaN基发光二极管光提取效率的有关研究.物理学报,vol.61, pp.208502-208502,2012.
[13]H.-Y. Ryu, "Large Enhancement of Extraction Efficiency in Thin-Film Photonic Crystal InGaN Light-Emitting Diode Structures," Journal of Korean Physical Society, vol.55, p. 2642.2009.
[1]Y. C. Shin, et al, "Effects of nanometer-scale photonic crystal structures on the light extraction from GaN light-emitting diodes," Quantum Electronics, IEEE Journal of, vol.46, pp.1375-1380,2010.
[2]C.-F. Chu, et al., "Study of GaN light-emitting diodes fabricated by laser lift-off technique," Journal of Applied Physics, vol.95, pp.3916-3922,2004.
[3]H.-M. An, et al., "Increased light extraction from vertical GaN light-emitting diodes with ordered, cone-shaped deep-pillar nanostructures," Quantum Electronics, IEEE Journal of, vol.48, pp.891-896,2012.
[4]B. Sun, et al., "Light extraction enhancement of bulk GaN light-emitting diode with hemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[5]P. Zhao and H. Zhao, "Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes," Optics express, vol.20, pp. Al65-A776,2012.
[6]T. Fujii, et al., "Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening," Applied Physics Letters, vol.84, pp.855-857,2004.
[7]Y. Wang, et al., "On the Radiation Profiles and Light Extraction of Vertical LEDs with Hybrid Nanorod and Truncated Microdome Surface Textures," 2013.
[8]J.-W. Pan and C.-S. Wang, "Light extraction efficiency of GaN-based LED with pyramid texture by using ray path analysis," Optics express, vol.20, pp. A630-A640,2012.
[9]L. Song Jae, "Analysis of light-emitting diodes by Monte Carlo photon simulation," Applied Optics, vol.40, pp.1427-37,20 March 2001.
[10]R. Windisch, et al., "Light-extraction mechanisms in high-efficiency surface-textured light-emitting diodes," Selected Topics in Quantum Electronics, IEEE Journal of, vol.8, pp. 248-255,2002.
[11]L. Song Jae, "Study of photon extraction efficiency in InGaN light-emitting diodes depending on chip structures and chip-mount schemes," Optical Engineering, vol.45, pp. 14601-1-14, Jan.2006.
[12]T. Hsueh, et al., "Enhancement in light output of InGaN-based microhole array light-emitting diodes," Photonics Technology Letters, IEEE, vol.17, pp.1163-1165,2005.
[13]C.-H. Chiu, et al., "Light Extraction Enhancement of GaN-Based Light-Emitting Diodes Using Crown-Shaped Patterned Sapphire Substrates," Photonics Technology Letters, IEEE, vol.24, pp.1212-1214,2012.
[14]R. Hu, et al., "Study on the optical properties of conformal coating light-emitting diode by Monte Carlo simulation," Photonics Technology Letters, IEEE, vol.23, pp.1673-1675, 2011.
[15]S. J. Lee, "Analysis of light-emitting diodes by Monte Carlo photon simulation," Applied Optics, vol.40, pp.1427-1437,2001.
[16]J.-B. Lee, et al., "Analysis of the extraction efficiency in GaN-on-sapphire light emitting diodes," in Numerical Simulation of Semiconductor Optoelectronic Devices,2006. NUSOD'06. International Conference on,2006, pp.17-18.
[17]T.-X. Lee, et al, "Light extraction analysis for GaN-based LEDs," in Integrated Optoelectronic Devices 2007,2007, pp.64731P-64731P-8.
[18]J. H. Son, et al., "Design Rule of Nanostructures in Light-Emitting Diodes for Complete Elimination of Total Internal Reflection," Advanced materials, vol.24, pp.2259-2262, 2012.
[19]D. Gao and Z. Zhou, "Nonlinear equation method for band structure calculations of photonic crystal slabs" Applied Physics Letters, vol.88, pp.163105-163105-3,2006.
[20]S. Wilson and M. Hutley, "The optical properties ofmoth eye'antireflection surfaces," Journal of Modern Optics, vol.29, pp.993-1009,1982.
[21]J. K. Kim, et al, "Light-Extraction Enhancement of GalnN Light-Emitting Diodes by Graded-Refractive-Index Indium Tin Oxide Anti-Reflection Contact," Advanced materials, vol.20, pp.801-804,2008.
[22]D.-S. Liu, et al, "Light-extraction enhancement in GaN-based light-emitting diodes using grade-refractive-index amorphous titanium oxide films with porous structures," Applied Physics Letters, vol.94, pp.143502-143502-3,2009.
[23]J.-Y. Cho, et al, "Forming the graded-refractive-index antireflection layers on light-emitting diodes to enhance the light extraction," Optics letters, vol.36, pp.3203-3205,2011.
[24]J. Mouchart, "Thin film optical coatings.1. Optical coating stabilities," Applied Optics, vol. 16, pp.2486-2490,1977.
[25]W. Zhou, et al., "Microstructured surface design for omnidirectional antireflection coatings on solar cells," Journal of Applied Physics, vol.102, pp.103105-103105-9,2007.
[26]J. Rayleigh, "The explanation of certain acoustical phenomena," Nature, vol.18, pp. 319-321,1878.
[27]W. H. Southwell, "Gradient-index antireflection coatings," Optics letters, vol.8, pp. 584-586,1983.
[28]J.-Q. Xi, et al, "Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection," Nature Photonics, vol.1, pp.176-179,2007.
[29]W. H. Southwell, "Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces," JOSAA, vol.8, pp.549-553,1991.
[30]J. K. Kim, et al, "GalnN light-emitting diode with conductive omnidirectional reflector having a low-refractive-index indium-tin oxide layer," Applied Physics Letters, vol.88, pp. 013501-013501-3,2006.
[31]C.-H. Chao, et al, "Influence of architecture-controlled GaN rod arrays on the output power of GaN LEDs," Photonics Technology Letters, IEEE, vol.22, pp.1847-1849,2010.
[32]H.-M. An, et al, "Increased light extraction from vertical GaN light-emitting diodes with ordered, cone-shaped deep-pillar nanostructures," Quantum Electronics, IEEE Journal of, vol.48, pp.891-896,2012.
[33]A. I. Zhmakin, "Enhancement of light extraction from light emitting diodes," Physics Reports, vol.498, pp.189-241,201
[34]T.-X. Lee, et al., "Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate," Optics express, vol.15, pp.6670-6676,2007.
[2]E. F. Schubert and J. K. Kim, "Solid-state light sources getting smart," Science, vol.308, pp. 1274-1278,2005.
[3]S. Nakamura, et al, "High-power GaN pn junction blue-light-emitting diodes," Japanese Journal of Applied Physics, vol.30, pp. L1998-L2001,1991.
[4]史光国.半导体发光二极管及固体照明.北京：科学出版社,2007.
[5]J. Kovac, et al., "Advanced light emitting diodes structures for optoelectronic applications," Thin solid films, vol.433, pp.22-26,2003.
[6]M. G. Craford, "LEDs for solid state lighting and other emerging applications:status, trends, and challenges," in Optics & Photonics 2005,2005, pp.594101-594101-10.
[7]H. J. Round, "A note on carborundum," Electrical world, vol.49, p.309,1907.
[8]B. Gudden and R. Pohl, "Das Quantenaquivalent bei der lichtelektrischen Leitung," Zeitschrift fur Physik A Hadrons and Nuclei, vol.17, pp.331-346,1923.
[9]H. Rupprecht, et al., "EFFICIENT VISIBLE ELECTROLUMINESCENCE AT 300°K FROM Ga 1-xAlxAs p-n JUNCTIONS GROWN BY LIQUID-PHASE EPITAXY," Applied Physics Letters, vol.11, pp.81-83,1967.
[10]H. Rupprecht, et al., "Efficient electroluminescence from GaAs diodes at 300 K," Applied Physics Letters, vol.9, pp.221-223,1966.
[11]N. Holonyak and S. Bevacqua, "Coherent (visible) light emission from Ga (Asl-xPx) junctions," Applied Physics Letters, vol.1, pp.82-83,1962.
[12]M. G. Craford and W. Groves, "Vapor phase epitaxial materials for LED applications," Proceedings of the IEEE, vol.61, pp.862-880,1973.
[13]E. F. Schubert, et al, Light emitting diodes:Wiley Online Library,2005.
[14]S. Nakamura, et al, "High-brightness InGaN/AlGaN double-heterostructure blue-green-light-emitting diodes," Journal of Applied Physics, vol.76, pp.8189-8191, 1994.
[15]S. Nakamura, et al, "Method of manufacturing p-type compound semiconductor," ed: Google Patents,1994.
[1]方志烈.半导体发光材料和器件.上海：复旦大学出版社,1992.
[2]A. David, "High-efficiency GaN-based light-emitting diodes:Light extraction by photonic crystals and microcavities," Ph. D. thesis, Ecole Polytechnique, Palaiseau, France,2006.
[3]周志敏.LED照明与工程设计.北京：人民邮电出版社,2010.
[4]K. Ramaiah, et al., "Characterization of InGaN/GaN multi-quantum-well blue-light-emitting diodes grown by metal organic chemical vapor deposition," Applied Physics Letters, vol.84, pp.3307-3309,2004.
[5]M. R. Krames, et al., "Status and future of high-power light-emitting diodes for solid-state lighting," Display Technology, Journal of, vol.3, pp.160-175,2007.
[6]A. I. Zhmakin, "Enhancement of light extraction from light emitting diodes," Physics Reports, vol.498, pp.189-241,2011.
[7]H. Amano, et al., "P-type conduction in Mg-doped GaN treated with low-energy electron beam irradiation (LEEBI)," Jpn. J. Appl. Phys, vol.28, pp. L2112-L2114,1989.
[8]S. Nakamura, et al., "Method of manufacturing p-type compound semiconductor," ed: Google Patents,1994.
[9]C. Wiesmann, "Nano-structured LEDs-Light extraction mechanisms and applications," 2010.
[10]S. P. DenBaars, et al, "Gallium nitride based light emitting diodes (LEDs) for energy efficient lighting and displays," in Electronics, Communications and Photonics Conference (SIECPC),2013 Saudi International,2013, pp.1-13.
[11]E. F. Schubert, et al, Light emitting diodes:Wiley Online Library,2005.
[12]M. G. Craford, "LEDs for solid state lighting and other emerging applications:status, trends, and challenges," in Optics& Photonics 2005,2005, pp.594101-594101-10.
[13]C.-F. Chu, et al, "High brightness GaN vertical light-emitting diodes on metal alloy for general lighting application," Proceedings of the IEEE, vol.98, pp.1197-1207,2010.
[14]O. Shchekin, et al, "High performance thin-film flip-chip InGaN-GaN light-emitting diodes" Applied Physics Letters, vol.89, pp.071109-071109-3,2006.
[15]S. Fan, et al, "High extraction efficiency of spontaneous emission from slabs of photonic crystals," Physical Review Letters, vol.78, p.3294,1997.
[16]R. K. Lee, et al, "Modified spontaneous emission from a two-dimensional photonic bandgap crystal slab," JOSA B, vol.17, pp.1438-1442,2000.
[17]马锡英.光子晶体原理及应用.北京：科学出版社,2010.
[18]Y. C. Shin, et al, "Effects of nanometer-scale photonic crystal structures on the light extraction from GaN light-emitting diodes," Quantum Electronics, IEEE Journal of, vol.46, pp.1375-1380,2010.
[19]K. McGroddy, et al, "Directional emission control and increased light extraction in GaN photonic crystal light emitting diodes," Applied Physics Letters, vol.93, pp. 103502-103502-3,2008.
[20]Y.-J. Lee, et al., "High light-extraction GaN-based vertical LEDs with double diffuse surfaces," Quantum Electronics, IEEE Journal of, vol.42, pp.1196-1201,2006.
[21]C.-C. Wang, et al., "Enhancement of the light output performance for GaN-based light-emitting diodes by bottom pillar structure," Applied Physics Letters, vol.91, pp. 121109-121109-3,2007.
[22]江洋等.柱状与孔状图形衬底对MOVPE生长GaN体材料及LED器件的影响.物理学报vol.58,pp.3468-3473,2009.
[23]H. Gao, et al., "Enhancement of the light output power of InGaN/GaN light-emitting diodes grown on pyramidal patterned sapphire substrates in the micro-and nanoscale," Journal of Applied Physics, vol.103, pp.014314-014314-5,2008.
[24]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[25]C.-H. Chao, et al, "Theoretical demonstration of enhancement of light extraction of flip-chip GaN light-emitting diodes with photonic crystals," Applied Physics Letters, vol.89, pp.091116-091116-3,2006.
[26]H. Kim, et al, "Light-extraction enhancement of vertical-injection GaN-based light-emitting diodes fabricated with highly integrated surface textures," Optics letters, vol. 33, pp.1273-1275,2008.
[27]S. H. Kim, et al, "An improvement of light extraction efficiency for GaN-based light emitting diodes by selective etched nanorods in periodic microholes," Optics express, vol. 21, pp.7125-7130,2013.
[28]B. Sun, et al, "Light extraction enhancement of bulk GaN light-emitting diode with hemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[29]Y. Wang, et al, "On the Radiation Profiles and Light Extraction of Vertical LEDs with Hybrid Nanorod and Truncated Microdome Surface Textures," 2013.
[30]W. Lee, et al, "Enhanced light output of GaN-based vertical light-emitting diodes with superimposed circular protrusions and hexagonal cones," Electrochemical and Solid-State Letters, vol.14, pp. H53-H56,2011.
[1]葛德彪,闫玉波.电磁波时域有限差分方法西安：西安电子科技大学出版社,2005.
[2]M. Moharam and T. Gaylord, "Rigorous coupled-wave analysis of planar-grating diffraction," JOSA, vol.71, pp.811-818,1981.
[3]N. Chateau and J.-P. Hugonin, "Algorithm for the rigorous coupled-wave analysis of grating diffraction," JOSA A, vol.11, pp.1321-1331,1994.
[4]M. Moharam, et al., "Stable implementation of the rigorous coupled-wave analysis for surface-relief gratings:enhanced transmittance matrix approach," JOSA A, vol.12, pp. 1077-1086,1995.
[5]刘军.科学计算中的蒙特卡洛策略.北京：高等教育出版社,2009.
[6]劳彩莲,”基于蒙特卡洛光线跟踪方法的植物三维冠层辐射传输模型[D],”北京：中国农业大学博士论文,2005.
[7]P. Johns, "Application of the transmission-line-matrix method to homogeneous waveguides of arbitrary cross-section," Electrical Engineers, Proceedings of the Institution of, vol.119, pp.1086-1091,1972.
[8]W. J. Hoefer, "The transmission-line matrix method--theory and applications," Microwave Theory and Techniques, IEEE Transactions on, vol.33, pp.882-893,1985.
[9]K. J. Bathe, "Finite element method," Wiley Encyclopedia of Computer Science and Engineering,2008.
[10]G. Dhatt and G. Touzot, Finite Element Method:John Wiley & Sons,2012.
[11]K. Yee, "Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media," Antennas and Propagation, IEEE Transactions on, vol.14, pp. 302-307,1966.
[12]A. Taflove and M. E. Brodwin, "Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations," Microwave Theory and Techniques, IEEE Transactions on, vol.23, pp.623-630,1975.
[13]G. Mur, "Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations," Electromagnetic Compatibility, IEEE Transactions on, pp.377-382,1981.
[14]J.-P. Berenger, "A perfectly matched layer for the absorption of electromagnetic waves," Journal of computational physics, vol.114, pp.185-200,1994.
[15]J.-P. Berenger, "Three-dimensional perfectly matched layer for the absorption of electromagnetic waves," Journal ofcomputational physics, vol.127, pp.363-379,1996.
[16]J. A. Roden and S. D. Gedney, "Efficient implementation of the uniaxial-based PML media in three-dimensional nonorthogonal coordinates with the use of the FDTD technique," Microwave and Optical Technology Letters, vol.14, pp.71-75,1997.
[17]J. A. Roden and S. D. Gedney, "Convolutional PML (CPML):An efficient FDTD implementation of the CFS-PML for arbitrary media," Microwave and Optical Technology Letters, vol.27, pp.334-338,2000.
[18]R. Courant and D. Hilbert, Methods of mathematical physics vol.1:Wiley, com,2008.
[19]G. L. L. Buffon and F. N. Egerton, Selections from Natural history general and particular vol.2:Arno Press New York,1977.
[20]雷桂媛,“关于蒙特卡洛及拟蒙特卡洛方法的若干研究[D],”浙江:浙江大学博士学位论文,2003.
[21]牟旷凝,“蒙特卡洛方法和拟蒙特卡洛方法在期权定价中应用的比较研究,”科学技术与工程pp.1925-1928,2010.
[22]Y.-K. Ee, et al., "Light extraction efficiency enhancement of InGaN quantum wells light-emitting diodes with polydimethylsiloxane concave microstructures," Opt. Express, vol.17, pp.13747-13757,2009.
[1]E. Yablonovitch, "Inhibited spontaneous emission in solid-state physics and electronics," Physical Review Letters, vol.58, p.2059,1987.
[2]S. John, "Strong localization of photons in certain disordered dielectric superlattices," Physical Review Letters, vol.58, pp.2486-2489,1987.
[3]V. Berger, et al, "Fabrication of a 2D photonic bandgap by a holographic method," Electronics Letters, vol.33, pp.425-426,1997.
[4]D.-H. Kim, et al, "Enhanced light extraction from GaN-based light-emitting diodes with holographically generated two-dimensional photonic crystal patterns," Applied Physics Letters, vol.87, pp.203508-203508-3,2005.
[5]C. Wiesmann, "Nano-structured LEDs-Light extraction mechanisms and applications," 2010.
[6]C. Wiesmann, et al., "Photonic crystal LEDs-designing light extraction," Laser & Photonics Reviews, vol.3, pp.262-286,2009.
[7]L. Hong-Wei, et al., "Light extraction enhancement of GaN LED with a two-dimensional photonic crystal slab," Chinese Physics Letters, vol.28, p.054216,2011.
[8]A. David, et al., "Photonic-crystal GaN light-emitting diodes with tailored guided modes distribution," Applied Physics Letters, vol.88, pp.061124-061124-3,2006.
[9]J. J. Wierer, et al., "Ⅲ-nitride photonic-crystal light-emitting diodes with high extraction efficiency," Nature Photonics, vol.3, pp.163-169,2009.
[10]E. Matioli and C. Weisbuch, "Impact of photonic crystals on LED light extraction efficiency: approaches and limits to vertical structure designs," Journal of Physics D:Applied Physics, vol.43, p.354005,2010.
[11]H. Kitagawa, et al, "Green GaInN photonic-crystal light-emitting diodes with small surface recombination effect," Applied Physics Letters, vol.98, pp.181104-181104-3,2011.
[12]Y.-W. Cheng, et al., "GaN-based LEDs surrounded with a two-dimensional nanohole photonic crystal structure for effective laterally guided mode coupling," Optics letters, vol. 36, pp.1611-1613,2011.
[13]马春生,刘式墉,光波导模式理论：吉林：吉林大学出版社,2007.
[14]A. Yariv and P. Yeh, Photonics:Optical Electronics in Modern Communications (The Oxford Series in Electrical and Computer Engineering):Oxford University Press, Inc., 2006.
[15]C. Xiong, et al, "Diffracted transmission effects of GaN and polymer two-dimensional square-lattice photonic crystals," Optics express, vol.17, pp.23684-23689,2009.
[16]B. Sun, et al., "Light extraction enhancement of bulk GaN light-emitting diode withhemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[17]H.-Y. Ryu, et al., "Enhancement of light extraction from two-dimensional photonic crystal slab structures," Selected Topics in Quantum Electronics, IEEE Journal of, vol.8, pp. 231-237,2002
[18]H. Gao, et al., "Improving light extraction efficiency of GaN-based LEDs by AlxGal-xN confining layer and embedded photonic crystals," 2012.
[19]杜刘革,“基于多GPU的FDTD并行算法及其在电磁仿真中的应用[D],”山东大学博士学位论文,2011.
[20]A. David, "High-efficiency GaN-based light-emitting diodes:Light extraction by photonic crystals and microcavities," Ph. D. thesis, Ecole Polytechnique, Palaiseau, France,2006.
[21]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[22]高晖等.双层光子晶体氮化镓蓝光发光二极管结构优化的研究.物理学报,vol.61, pp. 127807-127807,2012.
[1]许兴胜,陈弘达等.非晶光子晶体中的光子局域化.物理学报vol.55,pp.6430-6434,2006.
[2]K.-C. Kwan, et al, "Effects due to disorder on photonic crystal-based waveguides," Applied Physics Letters, vol.82, pp.4414-4416,2003.
[3]S. Mazoyer, et al., "Disorder-induced multiple scattering in photonic-crystal waveguides," Physical Review Letters, vol.103, p.063903,2009.
[4]H. De Raedt, et al, "Transverse localization of light," Physical Review Letters, vol.62, pp. 47-50,1989.
[5]Y. A. Vlasov, et al., "Different regimes of light localization in a disordered photonic crystal," Physical Review B, vol.60, p.1555,1999.
[6]朱志宏等.光子晶体的非严格周期性对其传输特性的影响.光学学报,vol.24, pp. 847-850,2004.
[7]D. H. Long, et al., "Analysis of disordered photonic crystal implemented in light-emitting diode for high light extraction efficiency," Japanese Journal of Applied Physics, vol.47, p. 4527.2008.
[8]D. H. Long, et al., "Design optimization of photonic crystal structure for improved light extraction of GaN LED," Selected Topics in Quantum Electronics, IEEE Journal of, vol.15, pp.1257-1263,2009.
[9]陈健等.光子晶体结构参数的随机扰动对光子晶LED出光效率的研究.光学学报,pp.233-236,2010.
[10]B. Wang, et al., "Effects of disorder in a photonic crystal on the extraction efficiency of a light-emitting diode,"Journal of Applied Physics, vol.106, pp.014508-014508-5,2009.
[11]L. Yan," Influence of Disordered Photonic Crystal on Light Extraction of a Kind of Light-emitting Diode Model," Acta Photonica Sinica, vol.6,2006.
[12]岳庆炀等.基于缺陷光子晶体结构的GaN基发光二极管光提取效率的有关研究.物理学报,vol.61, pp.208502-208502,2012.
[13]H.-Y. Ryu, "Large Enhancement of Extraction Efficiency in Thin-Film Photonic Crystal InGaN Light-Emitting Diode Structures," Journal of Korean Physical Society, vol.55, p. 2642.2009.
[1]Y. C. Shin, et al, "Effects of nanometer-scale photonic crystal structures on the light extraction from GaN light-emitting diodes," Quantum Electronics, IEEE Journal of, vol.46, pp.1375-1380,2010.
[2]C.-F. Chu, et al., "Study of GaN light-emitting diodes fabricated by laser lift-off technique," Journal of Applied Physics, vol.95, pp.3916-3922,2004.
[3]H.-M. An, et al., "Increased light extraction from vertical GaN light-emitting diodes with ordered, cone-shaped deep-pillar nanostructures," Quantum Electronics, IEEE Journal of, vol.48, pp.891-896,2012.
[4]B. Sun, et al., "Light extraction enhancement of bulk GaN light-emitting diode with hemisphere-cones-hybrid surface," Optics express, vol.20, pp.18537-18544,2012.
[5]P. Zhao and H. Zhao, "Analysis of light extraction efficiency enhancement for thin-film-flip-chip InGaN quantum wells light-emitting diodes with GaN micro-domes," Optics express, vol.20, pp. Al65-A776,2012.
[6]T. Fujii, et al., "Increase in the extraction efficiency of GaN-based light-emitting diodes via surface roughening," Applied Physics Letters, vol.84, pp.855-857,2004.
[7]Y. Wang, et al., "On the Radiation Profiles and Light Extraction of Vertical LEDs with Hybrid Nanorod and Truncated Microdome Surface Textures," 2013.
[8]J.-W. Pan and C.-S. Wang, "Light extraction efficiency of GaN-based LED with pyramid texture by using ray path analysis," Optics express, vol.20, pp. A630-A640,2012.
[9]L. Song Jae, "Analysis of light-emitting diodes by Monte Carlo photon simulation," Applied Optics, vol.40, pp.1427-37,20 March 2001.
[10]R. Windisch, et al., "Light-extraction mechanisms in high-efficiency surface-textured light-emitting diodes," Selected Topics in Quantum Electronics, IEEE Journal of, vol.8, pp. 248-255,2002.
[11]L. Song Jae, "Study of photon extraction efficiency in InGaN light-emitting diodes depending on chip structures and chip-mount schemes," Optical Engineering, vol.45, pp. 14601-1-14, Jan.2006.
[12]T. Hsueh, et al., "Enhancement in light output of InGaN-based microhole array light-emitting diodes," Photonics Technology Letters, IEEE, vol.17, pp.1163-1165,2005.
[13]C.-H. Chiu, et al., "Light Extraction Enhancement of GaN-Based Light-Emitting Diodes Using Crown-Shaped Patterned Sapphire Substrates," Photonics Technology Letters, IEEE, vol.24, pp.1212-1214,2012.
[14]R. Hu, et al., "Study on the optical properties of conformal coating light-emitting diode by Monte Carlo simulation," Photonics Technology Letters, IEEE, vol.23, pp.1673-1675, 2011.
[15]S. J. Lee, "Analysis of light-emitting diodes by Monte Carlo photon simulation," Applied Optics, vol.40, pp.1427-1437,2001.
[16]J.-B. Lee, et al., "Analysis of the extraction efficiency in GaN-on-sapphire light emitting diodes," in Numerical Simulation of Semiconductor Optoelectronic Devices,2006. NUSOD'06. International Conference on,2006, pp.17-18.
[17]T.-X. Lee, et al, "Light extraction analysis for GaN-based LEDs," in Integrated Optoelectronic Devices 2007,2007, pp.64731P-64731P-8.
[18]J. H. Son, et al., "Design Rule of Nanostructures in Light-Emitting Diodes for Complete Elimination of Total Internal Reflection," Advanced materials, vol.24, pp.2259-2262, 2012.
[19]D. Gao and Z. Zhou, "Nonlinear equation method for band structure calculations of photonic crystal slabs" Applied Physics Letters, vol.88, pp.163105-163105-3,2006.
[20]S. Wilson and M. Hutley, "The optical properties ofmoth eye'antireflection surfaces," Journal of Modern Optics, vol.29, pp.993-1009,1982.
[21]J. K. Kim, et al, "Light-Extraction Enhancement of GalnN Light-Emitting Diodes by Graded-Refractive-Index Indium Tin Oxide Anti-Reflection Contact," Advanced materials, vol.20, pp.801-804,2008.
[22]D.-S. Liu, et al, "Light-extraction enhancement in GaN-based light-emitting diodes using grade-refractive-index amorphous titanium oxide films with porous structures," Applied Physics Letters, vol.94, pp.143502-143502-3,2009.
[23]J.-Y. Cho, et al, "Forming the graded-refractive-index antireflection layers on light-emitting diodes to enhance the light extraction," Optics letters, vol.36, pp.3203-3205,2011.
[24]J. Mouchart, "Thin film optical coatings.1. Optical coating stabilities," Applied Optics, vol. 16, pp.2486-2490,1977.
[25]W. Zhou, et al., "Microstructured surface design for omnidirectional antireflection coatings on solar cells," Journal of Applied Physics, vol.102, pp.103105-103105-9,2007.
[26]J. Rayleigh, "The explanation of certain acoustical phenomena," Nature, vol.18, pp. 319-321,1878.
[27]W. H. Southwell, "Gradient-index antireflection coatings," Optics letters, vol.8, pp. 584-586,1983.
[28]J.-Q. Xi, et al, "Optical thin-film materials with low refractive index for broadband elimination of Fresnel reflection," Nature Photonics, vol.1, pp.176-179,2007.
[29]W. H. Southwell, "Pyramid-array surface-relief structures producing antireflection index matching on optical surfaces," JOSAA, vol.8, pp.549-553,1991.
[30]J. K. Kim, et al, "GalnN light-emitting diode with conductive omnidirectional reflector having a low-refractive-index indium-tin oxide layer," Applied Physics Letters, vol.88, pp. 013501-013501-3,2006.
[31]C.-H. Chao, et al, "Influence of architecture-controlled GaN rod arrays on the output power of GaN LEDs," Photonics Technology Letters, IEEE, vol.22, pp.1847-1849,2010.
[32]H.-M. An, et al, "Increased light extraction from vertical GaN light-emitting diodes with ordered, cone-shaped deep-pillar nanostructures," Quantum Electronics, IEEE Journal of, vol.48, pp.891-896,2012.
[33]A. I. Zhmakin, "Enhancement of light extraction from light emitting diodes," Physics Reports, vol.498, pp.189-241,201
[34]T.-X. Lee, et al., "Light extraction analysis of GaN-based light-emitting diodes with surface texture and/or patterned substrate," Optics express, vol.15, pp.6670-6676,2007.