For the study of the optical properties of porous silicon, self-standing layers with different porosities were studied. The optical constants (n, index of refraction and k, extinction coefficient) were determined from the experimental reflectance and transmittance spectra shown in Figs. 1.a and 1.b, respectively.
The increase in the porosity of porous silicon layer leads to a reduction in the optical reflectance and an increase in the transmittance as shown in Fig. 1. This behavior is attributed to the change in the morphology and the chemical composition difference between bulk silicon and porous silicon. Porous silicon can be described as an homogeneous mixture of air, amorphous silicon, silicon nanocrystallites and silicon dioxide [10]. Accordingly, the increase in the porosity leads to increased optical transparency of the membranes as portrayed in Fig. 1.b. Furthermore, the extremely low optical transmission of porous silicon in the 400 to 550 nm range is attributed to the very large absorption of porous silicon in the UV-visible region of the electromagnetic spectrum.
From the modeled R and T spectra, the optical constants n and k were calculated for self-standing porous silicon layers of different porosity were determined using a simulation program based on the matrix method. Figures 2.a and 2.b show the spectral index of refraction and the spectral extinction coefficient as a function of wavelength of nanoPS self-standing layers with three different porosities. The reduction in the size of the Si nanocrystals which compose nanoPS with increasing etching current density leads to a reduction in the effective index of refraction and, at the same time, an increase in the extinction coefficient. This behavior is attributed to the different morphology and chemical composition of nanoPS layers grown under different fabrication parameters. This tendency is in agreement with the previously reported behavior of the optical constants of Al2O3 and GaN porous layers, where a reduction in the index of refraction was observed with increasing porosity [18, 19].
From the experimental results of the extinction coefficient, the absorption coefficient can be calculated with the relationship,
$$\alpha =\frac{4\pi k}{\lambda } \left(1\right)$$
Figure 3 portraits the relation between the absorption coefficient as a function of wavelength for nanoPS layers of different porosities. In all cases, the graphs show a reduction in \(\alpha\) with increasing wavelength. In addition, α has higher values for low porosity samples (e.g. nanoPS 10 mA/cm2). This behavior is attributed to the reduction in the optical absorption at low porosity.
In addition, the values of the optical band gap for the nanoPS self-standing layers were extracted using Tauc plots [20]. Si is an indirect bandgap material in which the band gap energy equals 1.12 eV [21]. As has been previously demonstrated, the changes in the crystal structure and the morphology after etching the Si wafers to fabricate nanoPS lead to widening the optical bandgap and to a direct bandgap character [22]. Accordingly, the relation between \({\left(\alpha h\upsilon \right)}^{2}\) and photon energy (\(h\upsilon )\) was represented and is shown in Figs. 4.a, 4.b and 4.c for three self-standing layers with different porosities. The band gap energy value (\({E}_{g}\)) can be calculated by extrapolating the straight line of the relation between \({\left(\alpha h\upsilon \right)}^{2}\) and (\(h\upsilon )\). From the values of \({E}_{g}\) it is concluded that an increase in the porosity of the nanoPS layers leads to an increase in the value of the optical \({E}_{g}\). This behavior is attributed to the change in the composition from bulk Si to a matrix of air (pores), amorphous silicon and Si nanocrystals [10, 15, 23]. Accordingly, the optical properties of nanostructured porous silicon can be adjusted depending on the intended application by the change in the morphology and porosity of the bulk material.