The gallium nitride (GaN) light-emitting-diode (LED) top-bottom (or transmission-reflection) grating simulation results with error grating model are presented. The microstruc ture GaN bottom hole and top pillar gratings are calculated and compared with the non-grating (flat) case. Grating shapes simu lated are either conical or cylindrical. A direct comparison of 181 different combined transmission-reflection grating cases using the finite difference time domain method is presented. The simulation results show that simple or direct combinations of the optimized top grating with the optimized bottom grating only produce a 42% light extraction improvement compared to the non-grating case, which is much lower than that of an optimized single grating case. This is due to the mismatch of grating parameters with the direct addition of the second grating structure, which changes the optical field distribution in the LEDs. Therefore, it is very im portant to optimize both top and bottom gratings simultaneously for the double-grating design. We also show the optimization of a double grating structure can achieve better performance than a single grating. Finally, transmission-reflection error gratings are also presented. It is also the first time to present randomization in GaN LED grating design and its effects in fabrication. Our data shows that the favorable light extraction improvement is at approximately 10-15% randomization. The randomization can achieve 230% improvement over the original grating at a randomization intensity factor of 12.8%.

The Gallium Nitride (GaN) Light-Emitting-Diode (LED) bottom refection grating simulation and results are presented. A microstructure GaN bottom grating, either conical holes or cylindrical holes, was calculated and compared with the non-grating (flat) case. A time monitor was also placed just above the top of the LED to measure both time and power output from the top of the LED. Many different scenarios were simulated by sweeping three parameters that affected the structure of the micro-structure grating: unit cell period (Α) from 1 to 6 microns, unit cell width (w) from 1 to 6 microns, and unit cell grating height (d) from 50 to 200nm. The simulation results show that the cylindrical grating case has a 98% light extraction improvement, and the conical grating case has a 109% light extraction improvement compared to the flat plate case.

We study the top transmission grating's improvement on GaN LED light extraction efficiency. We use the finite difference time domain (FDTD) method, a computational electromagnetic solution to Maxwell's equations, to measure light extraction efficiency improvements of the various grating structures. Also, since FDTD can freely define materials for any layer or shape, we choose three particular materials to represent our transmission grating: 1) nonlossy p-GaN, 2) lossy indium tin oxide (ITO), and 3) non-lossy ITO (�=0). We define a regular spacing between unit cells in a crystal lattice arrangement by employing the following three parameters: grating cell period (�), grating cell height (d), and grating cell width (w). The conical grating model and the cylindrical grating model are studied. We also presented in the paper directly comparison with reflection grating results. Both studies show that the top grating has better performance, improving light extraction efficiency by 165%, compared to that of the bottom reflection grating (112%), and top-bottom grating (42%). We also find that when grating cells closely pack together, a transmission grating maximizes light extraction efficiency. This points our research towards a more closely packed structure, such as a 3-fold symmetric photonic crystal structure with triangular symmetry and also smaller feature sizes in the nano-scale, such as the wavelength of light at 460 nm, half-wavelengths, quarter wavelengths, etc.

We present simulation results of the indium tin oxide (ITO)