Estimation of the porosity and refractive index of sol–gel silica films using high resolution electron microscopy

Abstract

The relationship between the refractive index and the porosity of silica based anti-reflective coatings (ARCs) has been studied. The coatings were prepared with the traditional Stöber method. The refractive index was evaluated by fitting vis–NIR transmittance spectra to Fresnel׳s coefficient of reflection using the transfer matrix method. The porosity was assessed by a novel method based on image processing of high resolution scanning electron microscope (SEM) images. Results were compared to the commonly used Yoldas and Maxwell–Garnett mixing rules. Our results showed better agreement with the Yoldas mixing rule than with the Maxwell–Garnett mixing rule, which was explained as being due to the presence of elongated crack shaped pores in the ARCs rather than randomly dispersed spherical shaped pores, as was evident in the SEM images. Furthermore, we found that despite the presence of the elongated cracks, the coating appears to behave towards light like a homogenous medium. This somewhat surprising result calls for further research. Lastly, we have shown that it is reasonable to assume that the ARC is vertically homogeneous in terms of its porosity and effective refractive index.