为了提升氮化镓（GaN）蓝光发光二极管（LED）光提取效率，设计了双层光子晶体LED模型．提出等效折射率近似方法，简化求解了结构中的介质波导模式分布．从而对模型中顶层光子晶体刻蚀深度d，嵌入式光子晶体厚度T及其距有源层距离D等结构参数进行了优化．同时利用时域有限差分方法对优化结果进行了验证．相比其他仿真方法，模式分析极大地减小了对LED建模优化的计算复杂度，同时从理论上阐明了不同结构参数变化引起LED光提取效率改变的原因．研究发现，当顶层光子晶体满足d≈A／nPhCs时，结构内大部分高阶导模尚未被截断但源区能量向低阶导模的转化被有效抑制，光提取效率给出极大值．嵌入式光子晶体的引入将激发覆盖层模式，当满足100nm≤T≤300nm且100nm≤D≤200nm时，覆盖层模式可以从有源层获得较大能量并有效地与顶层光子晶体耦合，极大地提升了光提取效率．本文优化结果使得LED光提取效率提升了4倍，对高性能GaN蓝光LED的设计制造具有重要意义．%The GaN-based blue light LED with double layer photonic crystals is designed to enhance the vertical light extraction efficiency. The effective index approximation method is proposed and used to solve the distribution of the modes in the LED model. The geometrical parameters including the depth of the top photonic crystal d, the thickness of the embedded photonic crystal T, and the distance between the active layer and the embedded photonic crystal D are optimized. Compared with other numerical optimization, the mode analysis used in this work can dramatically save computation time and reduce complexity. In addition, it can provide more theoretical details about the influence of these geometrical parameters on light extraction efficiency. It can be found that when the surface photonic crystal satisfies the condition of d ~ A/nphcs, high order modes localized in the structure are still not cut off but the low order modes obtain less power since they are pushed away from the active layer. Hence, the light extraction efficiency reaches its maximum. The cap layer modes can be excited by the embedded photonic crystals, when this layer satisfies 100 nm ≤ T ≤ 300 nm and 100 nm ≤D ≤200 nm, the cap layer modes gather much power from the active layer and interact with the surface photonic crystals more efficiently. Hence the light extraction efficiency is dramatically improved. With our optimized parameters, the light extraction efficiency can be achieved to be up 4 times that of ordinary LED. These results shows a significant promise of designing a high-efficiency GaN-based blue light LED.
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