Modeling the partially detected backside reflectance of transparent substrates in reflectance microspectroscopy

Abstract

Thick transparent substrates are a key component for transmissive thin film optical filters and optoelectronics. In optical characterization of such substrates, light reflected from the backside — whether fully or partially detected — interferes with light directly reflected from the substrate’s front side. Herein, we introduce a straightforward approach for microspectroscopic measurements, with lateral dimensions in the micrometer range, to reliably assess the amount of measured backside reflectance. Therefore, geometric calculations based on micrographs, substrate thickness and refractive index, as well as magnification of the applied objective lens are utilized as input parameters. Additionally, we account for the influence of the numerical aperture, which is essential for accurate determination of the properties of thin films coated on thick transparent substrates. Compared to simulations completely incorporating or entirely neglecting the backside reflectance, our approach significantly reduces the mean squared error between measurement and model in the case of partially detected backside reflectance. After demonstrating the capabilities of our approach to accurately identify the amount of backside reflectance detected for a variety of bare transparent substrate materials, thicknesses, and objective lenses, we prove the capacity to determine the thickness of silicon nitride and silicon nitride/silicon oxide layers on glass substrates with high consistency to complementary STEM/EDX measurements even for large numerical apertures.