Nanowires array designed by means of two-dimension closed-form solution for antireflection

Abstract

By investigating the difference between the analytic solutions obtained from commonly used two-dimensional effective medium theory and the numerical solutions, we found that any analytical solution was quite accurate only at its right normalized cycle, determined by its own effective range. Thus, one should solve the problem that there was no closed-form solution for the effective permittivity of a two-dimensional zero-order grating, and expand the applied scope of the effective medium theory to the boundary of zero-order diffraction. Secondly, by using the two-dimensional analytical solution, we have designed a nanowires anti-reflection layer in silicon, which fully meet the needs of the design that reach zero reflectance at 650 nm; and the spectrum averaged reflection from 310-1120 nm is 8%, lower than silicon nitride anti-reflection layer 9.9%. Stavenga formula can be used to design a large normalized period antireflective microstructure, while the Maxwell-Garnett formula can be used to design a small normalized cycle antireflective microstructure. Design of antireflection structure by two-dimensional closed form solution directly is viable, which have huge potential application value.