Effective optical response of silicon to sunlight in the finite-difference time-domain method

Abstract

The frequency dependent dielectric permittivity of dispersive materials is commonly modeled as a rational polynomial based on multiple Debye, Drude, or Lorentz terms in the finite-difference time-domain (FDTD) method. We identify a simple effective model in which dielectric polarization depends both on the electric field and its first time derivative. This enables nearly exact FDTD simulation of light propagation and absorption in silicon in the spectral range of 300-1000 nm. where ε ∞ is permitivitty at infinite frequency, and a p;j , b p;j are real fitting coefficients that do not necessarily have a physical meaning. There are recent reports on successful application of the critical point model (with a p;1 ≠ 0) for the description of the dielectric function of gold [6,7], silver [7,8], aluminum, and chromium [7] in the wide wavelength range. This model was implemented in FDTD with the help of the recursive convolution (RC) technique [9]. Dispersion profiles of complex materials cannot always be fitted using a small number, P, of terms in (1). Alternately, one can divide the required wavelength range into subranges for separate fittings in each subrange. In this case, multiple FDTD simulations should be performed, followed by merging of the separate results. This makes simulation cumbersome and inefficient.In traditional fitting, each dielectric susceptibility term (2) consists of either a single imaginary pole (Debye model), two complex poles (Lorentz model), or an imaginary pole plus pole at zero (Drude model) in the complex ω-plane. More flexible fitting (some of which is captured in the critical point model [5]

Passivation of all-angle black surfaces for silicon solar cells

“…The commercial Lumerical FDTD Solutions package is used for the simulations performed in this work. Literature on FDTD simulations of NWs has already shown significant reduction in reflection which is attributed to guided modes, Bloch modes and Fabry-Perot resonances [29][30][31]. Furthermore, it is shown that the geometrical properties of the NW arrays (NWAs) strongly influence the emergence of such modes [13].…”

Using metallic photonic crystals as visible light sources

“…For large simulations the method is parallelized via domain decomposition and scales almost linearly with the number of used CPUs [33]. Absorbing materials are simulated by fitting the experimental complex dielectric function by a number of Drude-Lorentz [32] or modified Lorentz [34] terms. There is no restriction on the form of scatterers in FDTD, however a special treatment of fine structures such as thin material interfaces is sometimes required [35].…”

Optimization of Lorentz model parameters for crystalline AS<inf>2</inf>S<inf>3</inf>, SiC and modified Lorentz model parameters for nanocrystalline SiO

“…where, ε∞ is permittivity at infinite frequency, ωp is the pole pair frequency, γp is the damping coefficient , Δεp is the change in relative permittivity due to change in p'th pole and εs is zero frequency relative permittivity [3]. Here, ωp, γp , γ'p are in 1/μm and speed of light is unity.…”