Exact comprehensive equations for the photon management properties of silicon nanowire

Unique photon management (PM) properties of silicon nanowire (SiNW) make it an attractive building block for a host of nanowire photonic devices including photodetectors, chemical and gas sensors, waveguides, optical switches, solar cells, and lasers. However, the lack of efficient equations for the quantitative estimation of the SiNW's PM properties limits the rational design of such devices. Herein, we establish comprehensive equations to evaluate several important performance features for the PM properties of SiNW, based on theoretical simulations. Firstly, the relationships between the resonant wavelengths (RW), where SiNW can harvest light most effectively, and the size of SiNW are formulized. Then, equations for the light-harvesting efficiency at RW, which determines the single-frequency performance limit of SiNW-based photonic devices, are established. Finally, equations for the light-harvesting efficiency of SiNW in full-spectrum, which are of great significance in photovoltaics, are established. Furthermore, using these equations, we have derived four extra formulas to estimate the optimal size of SiNW in light-harvesting. These equations can reproduce majority of the reported experimental and theoretical results with only ~5% error deviations. Our study fills up a gap in quantitatively predicting the SiNW's PM properties, which will contribute significantly to its practical applications.