
\begin{abstract}

    GeSn alloys have attracted significant interest due to their potential applications in next-generation optoelectronic, transport and spintronic devices. The incorporation of Sn into Ge results in a direct bandgap semiconductor, which is crucial for efficient light emission and absorption in photonics, as well as high-mobility transistors. Additionally, GeSn’s compatibility with existing silicon technology makes it a promising candidate for monolithic integration with CMOS platforms. GeSn has also emerged as a potential material for spintronic applications due to its strong spin-orbit coupling and tunable electronic structure, which could enable efficient spin manipulation and transport.

    However, despite these advantages, the study of GeSn remains limited due to challenges in material synthesis, such as the low solubility of Sn in Ge and the metastable nature of GeSn alloys. These factors complicate the growth of high-quality, defect-free GeSn films, limiting a comprehensive understanding of its structural, electronic, optical, and spintronic properties. Consequently, more research is needed to fully explore its potential for advanced technological applications.

    In this thesis, we present a novel theoretical framework for understanding GeSn by investigating three key properties: (i) electronic transport, (ii) spintronic behaviour, and (iii) optoelectronic characteristics.

    To fully understand its potential in transport applications, we use first-principles electronic-structure theory to calculate the intra- and intervalley electron-alloy scattering parameters of n-type GeSn. These parameters are used to determine the alloy scattering contributions to the n-type electron mobility of GeSn, which we calculate as functions of Sn concentration and temperature using a first iteration of the Boltzmann transport equation in the relaxation time approximation. For unstrained GeSn, we find that at $300$K, a Sn concentration of at least $13.5\%$ is needed to achieve an electron mobility greater than that of Ge. Our results show that the room-temperature mobility of GeSn can be over $25$ times higher than the mobility of Ge, while at $15$K, under $1\%$ biaxial tensile strain, less than $6\%$ Sn incorporation into Ge quadruples its mobility. Applying biaxial tensile strain to GeSn further increases the mobility and at a lower Sn content than in unstrained GeSn.

     We also calculate the electron spin-alloy scattering parameters and the electron spin-phonon scattering parameters in n-type GeSn alloys from first-principles methods. These parameters are used in calculating the electron-alloy and electron-phonon scattering contributions to the n-type spin relaxation of GeSn, as functions of alloy content, strain, and temperature. Our findings show that the spin-relaxation time of Ge can be substantially increased upon the introduction of sufficient Sn. For unstrained, room-temperature GeSn, we find that a Sn concentration of at least $10\%$ is required to achieve a spin relaxation time greater than Ge, with $17\%$ Sn needed to increase the spin relaxation time from the nanosecond range to the microsecond range. At low temperatures (30K), the addition of $10\%$ Sn can increase the spin relaxation time from $10^{-7}$s to 0.1s. Similar to the behaviour of the electron mobility, the application of biaxial tensile strain to GeSn increases the spin relaxation time further and at a lower Sn content compared to unstrained GeSn.

    Finally, we investigate the optoelectronic properties of GeSn alloys by calculating the absorption coefficient and photoluminescence as functions of photon energy and temperature for fixed Sn concentrations in the short-wave infrared (SWIR) light range (0.4-1eV). Our approach combines degenerate and non-degenerate perturbation theory to accurately account for both direct and indirect optical transitions, representing the first study to incorporate alloy scattering in the modelling of an alloy’s optical properties. We find that both absorption and emission increase with Sn content. In particular, incorporating $12\%$ Sn into Ge enhances the photoluminescence intensity by a factor of 250 compared to pure Ge, while the absorption coefficient at this concentration approaches $10^5\ $cm$^{-1}$ within the SWIR range. While indirect transitions contribute minimally to absorption, particularly below the direct bandgap, they play a dominant role in light emission in indirect-gap GeSn, where alloy scattering is found to be more significant than electron–phonon interactions. 
    
    This work represents a significant step forward in the theoretical understanding of GeSn alloys, offering new insights into their transport, spintronic, and optical responses, and opening pathways for their deployment in advanced electronic and photonic devices.

    
\end{abstract}