Size-dependent spectral transmittance of crystalline silicon from bulk regimes to the quantum-confined

Abstract

It is necessary to distinguish between inherent changes in silicon's electrical structure and geometric size effects in order to comprehend the transition from bulk-like optical activity to quantum-confined behavior. Here, a size-dependent band-gap model, the Tauc relation, and the Beer-Lambert law are used to investigate the absorption coefficient and spectral transmittance over five size regimes ranging from 100 μm to 1 nm. The findings show that this evolution is governed by two different mechanisms. The absorption coefficient essentially stays bulk-like from the micrometer scale down to tens of nanometers, whereas transmittance gradually increases mostly due to the shorter optical path length. In the 1–10 nm regime, however, quantum confinement modifies the energy gap and absorption spectrum, making the optical response intrinsically size dependent. Comparison with available experimental and reference data shows good qualitative agreement in the spectral trends. The results therefore distinguish thickness-induced transmission enhancement from genuine quantum-confinement effects and provide a continuous framework for describing and tuning the optical response of silicon through dimensional control in photonic and optoelectronic applications.