Title: Electronic and structural properties of group IV materials and their polytypes

Abstract: Nanotechnology's impact on semiconductor industry advancement, particularly through the engineering of nanostructures like nanowires, opens new possibilities for material functionality due to the tunable physical properties of nanostructures compared to bulk materials. This paper presents a comprehensive study on group IV semiconductors and their binaries across four polytypes: 2H, 3C, 4H, and 6H, focusing on their optoelectronic application potential. Deep understanding of these polytypes is particularly relevant for nanowire-based technologies. Through first principles modeling, we examine the structural and electronic properties of these materials, emphasizing their band structure, stability, and the feasibility for light-emitting applications. We use a generalized Ising model to discuss materials stability and tendency for polytypism. We also determine relative band edge positions and employ a six $k\cdot p$ model for a detailed understanding of the materials' electronic properties. Due to the comprehensive nature of this study, we provide insight on the chemical trends present in all of the studied properties. Our theoretical predictions align well with existing experimental data, suggesting new avenues for nanostructure-based device development. The discussion extends to the implications of these findings for the fabrication of optoelectronic devices with the studied IV-IV materials, highlighting the challenges and opportunities for future research in nanowire synthesis and their application.