Optical Bandgap of Amorphous Germanium Quantum Wells

The study provides a systematic and quantitative comparison of optical bandgap determination methods for amorphous germanium (a-Ge) ultra-thin films, revealing significant limitations in traditional approaches. The widely used single-pass absorption model, which assumes light absorption follows a simple Beer-Lambert exponential decay, introduces errors in thin films due to neglecting multiple internal reflections. By developing a multiple-reflection interference model, this work demonstrates a more accurate way to extract the absorption coefficient and, consequently, the optical bandgap. This methodological improvement is critical for ensuring that reported bandgap values reflect intrinsic material properties rather than artifacts of measurement techniques.

A key finding is the superiority of the Cody model over the Tauc model for bandgap extraction in a-Ge films. The Tauc plot, a staple in amorphous semiconductor research, is shown to suffer from energy-dependent slope variations, making it prone to subjective fitting choices that can lead to inconsistent results. In contrast, the Cody model provides a more linear absorption behavior near the band edge, yielding more reliable and reproducible bandgap values. This work challenges conventional assumptions in thin-film optical analysis and suggests a shift toward Cody-based bandgap determination, particularly for ultra-thin absorbing materials.

The research also highlights the role of quantum confinement effects in ultra-thin amorphous germanium layers, a topic that has received limited experimental attention. By systematically varying film thicknesses down to 2 nm, the study confirms a significant blue shift in the optical bandgap as layer thickness decreases, consistent with quantum size effects. However, when germanium is embedded in multi-layered (ML) a-Ge/SiO₂ structures, the expected quantum confinement is mitigated due to electronic coupling between adjacent layers. This finding has profound implications for the design of engineered nanostructures, as it suggests that superlattice architectures can be used to tune optical properties beyond what is achievable in isolated thin films.

Beyond fundamental insights, this work has direct applications in optoelectronics, photovoltaics, and photonic coatings. Amorphous semiconductors, including a-Ge, are key materials for thin-film transistors, infrared detectors, and photonic devices. The improved bandgap determination methods proposed here enable more precise optical modeling, which is essential for optimizing device performance. Additionally, the ability to control the optical bandgap in layered structures opens new possibilities for designing nanoscale heterostructures with tailored absorption properties, crucial for high-efficiency light-harvesting applications.

Overall, this study makes a critical contribution to the field of optical characterization of amorphous semiconductors, offering both theoretical advancements and practical methodologies for experimentalists. By addressing inaccuracies in bandgap determination, introducing a superior optical modeling framework, and elucidating quantum confinement effects in ultra-thin a-Ge films, this work sets a new standard for the optical analysis of disordered nanostructured materials. Future research building on these findings could further refine quantum confinement models and explore their implications for emerging nanophotonic and quantum optical technologies.

Multi-Reflection Interference Model – This approach enhances the precision of absorption coefficient measurements compared to the conventional single-pass method, which often underestimates absorption in thin films.

Reliable Bandgap Extraction – A comparison of traditional and advanced optical models reveals that the Cody plot provides a more accurate bandgap estimation than the commonly used Tauc plot, which can introduce inconsistencies.

Quantum Confinement Effects – Ultra-thin a-Ge films (≤10 nm) exhibit a blue shift in the optical bandgap as the result of quantum confinement, while multi-layered structures experience weaker confinement due to electronic wavefunction overlap between adjacent layers.

Applications & Impact – The findings contribute to the development of advanced optoelectronic materials, such as engineered coatings, sensors, and semiconductor devices requiring precise optical characterization at the nanoscale.