Analysis of the sinusoidal nanopatterning grating structure

To accurately utilize the sinusoidal nanopatterning grating structure for greatly improving the light extraction efficiency of light-emitting diodes, the transmittance characteristics of these nanostructures as a function of the normalized period and the normalized depth are investigated quantitatively. It is found that when the normalized period of nanostructure is less than 0.46; in other words, only zeroth order transmission light is propagating, the light extraction efficiency can be enhanced immensely due to the higher transmittance of surface structure. When the period scale of nanostructure is more than the emitted wavelength, the transmittances decrease as the structure height increase. However, as the period dimension is less than the emitted wavelength, the transmittance of surface profile is increased as the depth increases. Besides, in order to easily analyze and effectively design the transmittance characteristics of these nanopatterning structures integrated in LEDs, we propose that the developed scalar method and the effective medium theory can be used accurately. The accuracy of both uncomplicated methods is quantitatively evaluated by the comparison of diffraction efficiencies predicted by the scalar theory and effective medium method, to exact results calculated by the rigorous coupled wave analysis method.

► We investigate mainly the transmittance of the internal reflective sinusoidal grating.
► The scalar diffraction theory is proposed to analyze the transmittivity of grating.
► The effective medium theory is applied to design the grating microstructure.
► The accuracy of these both uncomplicated methods is quantitatively evaluated.