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.

In this paper, we use a Finite-Difference Time-Domain GaN LED model to study constant wave (CW) average power of extracted light. The stmcture simulated comprises of a 200tm1-thick p-GaN substrate, 50nm-thick MQW, 400nm-thick n-GaN substrate, and a 200run n-GaN two-dimensional Photonic Crysta1(2PhC) !,>rating. We focus on optimizing three design parameters: grating period (A), grating height (d), and fill factor (FF). In the primary set of simulations, we fix the fill factor at 50% and simulate ten different grating periods (100 to lOOOnm in steps of lOOnm) and four different !,>rating heights (50 to 200tm1 in steps of 50nm), ~md calculate the average power output of the device. The results from these simu. lations show that for both conical and cylindrical gratings, the maxmium light ex1.raction improvement occurs when A = lOOnm. In the second set of simulations, we maintain a constant grating period A= lOOnm and sweep the fill factor from 25 to 75%. The results of these simulations show that the fill factor affects clyindrical and conical gratings differently. As a whole, we see that the nano-structure grating mostly depends on period, but also depends on height and fi ll factor. The grating structure improves light extraction in some cases, but not all.

We study solar-cell designs using nano-grating on both top (transmission) and bottom (reflection) of the solar cell. First, we perform simulations based on rigorous coupled wave analysis (RCWA) to evaluate the diffraction top gratins. In RCWA method, we calculate up to 20 harmonics, and sweep the launch angle of incident light from 0 to 90 degree. The incident light varies from100nm to 1200nm wavelength. Triangular grating can achieve higher light absorption compared to the rectangular grating. The best top grating is around 200nm grating period, 100nm grating height, and 50% filling factor, which responses to 37% improvement for triangular grating and 23% for rectangular grating compared to non-grating case. Then, we use Finite-Difference Time-Domain (FDTD) to simulate transmission/reflection double grating cases. We simulated triangular-triangular (top-bottom) grating cases and triangular-rectangular (topbottom) grating case. We realize solar cell efficiency improvement about 42.4%. For the triangulartriangular (top-bottom) grating case, the 20% efficiency improvement is achieved. Finally, we present weighted-light simulation for the double grating for the first time and show the best grating can achieve 104% light improvement, which is quite different from traditional non-weighted calculation.

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