Revisiting the optical bandgap of semiconductors and the proposal of a unified methodology to its determination

Abstract

Along the last two centuries, the story of semiconductor materials ranged from a mix of disbelief and frustration to one of the most successful technological achievements ever seen. Such a progress comprised the development of materials and models that, allied to the knowledge provided by spectroscopic techniques, resulted in the (nowadays) omnipresent electronic gadgets. Within this context, optically-based methods were of special importance since, amongst others, they presented details about the electronic states and energy bandgap E gap of semiconductors which, ultimately, decided about their application in devices. Stimulated by these aspects, this work investigated the semiconductors silicon, germanium, and gallium-arsenide in the crystalline (bulk and powder) and amorphous (film) forms. The detailed analysis of the experimental results indicates that accurate E gap values can be obtained by fitting a sigmoid (Boltzmann) function to their corresponding optical absorption spectra. The method is straightforward and, contrary to the traditional approaches to determine E gap, it is exempt from errors due to experimental spectra acquisition and data processing. Additionally, it complies with the requirements of direct, indirect, and amorphous bandgap semiconductors, and it is able to probe the (dis)order of the material as well. In view of these characteristics, a new−unified methodology based on the fitting of the absorption spectrum with a Boltzmann function is being proposed to efficiently determine the optical bandgap of semiconductor materials.