Date of Award


Degree Name

MS in Electrical Engineering


Electrical Engineering


Xiaomin Jin


Gallium nitride (GaN) light emitting diodes (LED) embody a large field of research that aims to replace inefficient, conventional light sources with LEDs that have lower power, higher luminosity, and longer lifetime. This thesis presents an international collaboration effort between the State Key Laboratory for Mesoscopic Physics in Peking University (PKU) of Beijing, China and the Electrical Engineering Department of California Polytechnic State University, San Luis Obispo. Over the course of 2 years, Cal Poly’s side has simulated GaN LEDs within the pure blue wavelength spectrum (460nm), focusing specifically on the effects of reflection gratings, transmission gratings, top and bottom gratings, error gratings, 3-fold symmetric photonic crystal, and 2-fold symmetric nano-imprinted gratings. PKU used our simulation results to fabricate GaN high brightness LEDs from the results of our simulation models. We employed the use of 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. Since the FDTD method was based on the differential form of Maxwell’s equations, it arbitrarily simulated complex grating structures of varying shapes and sizes, as well as the reflection, diffraction, and dispersion of propagating light throughout the device.

We presented the optimized case, as well as the optimization trend for each of the single grating structures within a range of simulation parameters on the micron scale and find that single grating structures, on average, doubled the light extraction efficiency of GaN LEDs. Photonic crystal grating research in the micron scale suggested that transmission gratings benefit most when grating cells tightly pack together, while reflection gratings benefit when grating cells space further apart. The total number of grating cells fabricated on a reflection grating layer still affects light extraction efficiency. For the top and bottom grating structures, we performed a partial optimization of the grating sets formed from the optimized single grating cases and found that the direct pairing of optimized single grating structures decreases overall light extraction efficiency. However, through a partial optimization procedure, top and bottom grating designs could improve light extraction efficiency by 118% for that particular case, outperforming either of the single top or bottom grating cases alone. Our research then explored the effects of periodic, positional perturbation in grating designs and found that at a 10-15% randomization factor, light extraction efficiency could improve up to 230% from the original top and bottom grating case. Next, in an experiment with PKU, we mounted a 2-fold symmetric photonic crystal onto a PDMS hemi-cylinder by nano-imprinting to measure the transmission of light at angles from near tangential to normal. Overall transmission of light compared with the non-grating design increases overall light extraction efficiency when integrated over the range of angles. Finally, our research focused on the 3-fold symmetric photonic crystal grating structure and employed the use of 3-D FDTD methods and incoherent light sources to better study the effects of higher-ordered symmetry in grating design. Grating cells were discovered as the source of escaping light from the GaN LED model. The model revealed that light extraction efficiency and the far-field diffraction pattern could be estimated by the position of grating cells in the grating design.