Assessment of effective-medium theories in the analysis of nucleation and microscopic surface roughness evolution for semiconductor thin films

Real-time spectroscopic ellipsometry (SE) data collected during the nucleation and growth of hydrogenated amorphous silicon (a-Si: H) thin films have been analyzed by applying one and two layer optical models incorporating different effective medium theories (EMT's). The purpose of the EMT's is to simulate the dielectric functions of the microscopically inhomogeneous nucleating and surface roughness layers used in the models. Five one-parameter EMT's have been considered in this study for the characterization of three classes of microscopically inhomogeneous layers, including (i) 5--20 -thick nucleating layers consisting of isolated a-Si: H clusters on the underlying substrate, (ii) 10--15 -thick nucleation-induced surface roughness layers on very thin (200) a-Si: H films, and (iii) 40--80 -thick substrate-induced surface roughness layers on thicker (>2500) a-Si: H films. In all three applications, the Bruggeman effective medium approximation (EMA) provides the best overall fits to the time evolution of the SE data, and complexities beyond the simple one-parameter EMA cannot be justified in view of existing experimental limitations. Furthermore, many of the general features of nucleation, coalescence, and bulk layer growth deduced in the SE analysis and used in previous studies to understand and optimize materials and device fabrication, are found to be essentially independent of the EMT used in the analysis.