Effect of Spherical Particle Coating on the Efficiency of Anti-reflective Film

The anti-reflective behavior of a layer of mono-dispersed spherical particles coated onto a substrate is analyzed theoretically. The coated particles are divided into multiple layers each plays the role of a film, and the overall reflectivity is estimated by the anti-reflective theorem for a single film. Numerical simulations are conducted in which the particle material is SiO2 mixed with TiO2 or appropriate polymers such as polystyrene. We show that both the reflectivity and the transmittivity of the system vary with the refractive index of the particle and that of substrate. For particles of radius 40 nm and refractive index 1.35, the reflectivity has the minimum value of 0.0068 % at 389 nm. The results of reflectance by RCWA and EMT in the case of particles of radius 40 nm, refractive index 1.46 have similar tendency on visible wavelength. The reasons of inaccuracy are possible for that when the period of spherical particles is not enough smaller than incident wavelength, and we work out differential equations, harmonics is insufficient.