Optical bandgap of single- and multi-layered amorphous germanium ultra-thin films

Accurate optical methods are required to determine the energy bandgap of amorphous semiconductors and elucidate the role of quantum confinement in nanometer-scale, ultra-thin absorbing layers. Here, we provide a critical comparison between well-established methods that are generally employed to determine the optical bandgap of thin-film amorphous semiconductors, starting from normal-incidence reflectance and transmittance measurements. First, we demonstrate that a more accurate estimate of the optical bandgap can be achieved by using a multiple-reflection interference model. We show that this model generates more reliable results compared to the widely accepted single-pass absorption method. Second, we compare two most representative methods (Tauc and Cody plots) that are extensively used to determine the optical bandgap of thin-film amorphous semiconductors starting from the extracted absorption coefficient. Analysis of the experimental absorption data acquired for ultra-thin amorphous germanium (a-Ge) layers demonstrates that the Cody model is able to provide a less ambiguous energy bandgap value. Finally, we apply our proposed method to experimentally determine the optical bandgap of a-Ge/SiO2 superlattices with single and multiple a-Ge layers down to 2 nm thickness.