Bruggeman effective medium approach for modelling optical properties of porous silicon: comparison with experiment

Abstract

While numerous works deal with the properties and applications of porous silicon (PS), some of the related topics are not complete or could be investigated from different aspects. The main objective of this paper is to provide novel information associated with the optical properties of nano-and meso-PS by studying the variation of the effective refractive index (n eff ) and the relative dielectric constant (ε r,eff ) as a function of porosity. For this purpose various PS samples were prepared by electrochemical etching of p and p + -type silicon wafers in order to form silicon supported nano-PS and free-standing meso-PS layers, respectively. The experimental effective optical parameters (n eff , ε r,eff ) of the meso-PS films, were determined from the transmission spectra and the Bragg law. While, in the case of nano-PS layers, we applied the Goodman method, and deduced the values of n eff and ε r,eff from the Bruggeman's effective medium approximation (EMA). In the EMA calculation, the PS structure was considered as being a physical combination of three distinct phases formed by silicon, silicon dioxide and voids with a convenient volume fraction. A good agreement between theory and experiment was found in the case of silicon-supported nano-PS for all porosities. However, for free-standing meso-PS, the theory does not well fit the experimental results for porosities lower than 50% and higher than 70%.

Passive PT Symmetry in Organic Composite Films via Complex Refractive Index Modulation

“…In both cases, the real and imaginary refractive index components vary approximately linearly with composition in accord with a simple Bruggeman effective medium approximation (EMA; dashed lines). [ 17 ] The range of complex indices accessible with the full three-component 'optical alloy' systems is summarized in the n-k plane for a wavelength of λ = 532 nm in Figure 2 c. Here, the pure material indices (large dots) constitute the vertices of a skewed triangle (light blue shaded region) that bounds all complex index combinations achievable with different alloy compositions; DCM concentration was limited to 44% because this yields suffi cient extinction and minimizes crystallization.…”

Simulations and Analysis of Nano Scale Porous Silicon Structures for Optical Sensor Applications

“…These parameters are the base of the simulations and analysis of 1D-PSPBG structures. Refractive index of the 1D-PSPBG layers with the porosity is related by BEMA model [18]. This approximation is acceptable because the size of the pore is much smaller than the wavelengths of incidence light in the near UV-VIS-IR regions.…”

Near Field Heat Transfer between Random Composite Materials: Applications and Limitations

“…Examples of EMA include the Maxwell-Garnett approximation, the Bruggeman approximation [8] that is symmetric with respect to the exchange of host and inclusions, thus making it more appropriate for random porous media [9]. EMAs are not unique and there are at least a dozen different models or recipes described in the literature to obtain the effective dielectric function.…”

“…In both cases, classical models such as MaxwellGarnett or Bruggeman do not fit the experimental data and a modification to the Maxwell-Garnett model was proposed. However, there are cases where the theoretical description of the optical properties using EMA and experiments match, such as in porous Si whose measured optical response, is described accurately by the Bruggeman model [9] or the calculation of the extinction coefficient of nested nanoparticles can be described by Maxwell-Garnett model [15].…”