\chapter{Summary, Conclusions and Outlook} \label{chap:conc}

% 4-5 pages is plenty

\section{Summary and Conclusions}

This thesis has delivered a detailed theoretical analysis of the transport, spintronic, and optical properties of GeSn alloys, advancing our understanding of this emerging group-IV semiconductor. 

To understand the electronic transport properties of GeSn, we carried out a full \textit{ab initio} calculation of n-type intra- and intervalley alloy scattering parameters for GeSn alloys, using supercell methods to numerically represent the alloy scattering problem. These parameters, which were previously unknown and difficult to determine from experiments, were up to 3-4 times larger than another group-IV alloy in SiGe. In particular, intravalley scattering in the $L$ and $\Gamma$ valleys, as well as intervalley scattering between the $L$ valleys and $\Gamma$ and $L$ are prominent. This evidence alone suggests alloy scattering should significantly impact on the transport properties of GeSn.

We used our calculated scattering parameters with phonon parameters from the literature in the Boltzmann Transport Equation to find the n-type mobility of GeSn as a function of Sn concentration, temperature and biaxial tensile strain. Our results shows that previous calculations of the mobility have been overestimations, as the effects of alloy scattering were not fully considered, and the mobility is significantly limited by alloy scattering. Nonetheless, sufficient addition of Sn to Ge beyond a threshold composition causes the mobility to increase by up to 25 times the room-temperature value. Applying biaxial tensile strain reduces the Sn content necessary to invoke an increase of this magnitude. Our findings could prompt further work on GeSn transistors. 



% spin scattering 
In the second part of this thesis, we calculated the key spin-dependent alloy scattering and electron-phonon scattering parameters of GeSn. Our findings indicate that electrons undergo spin polarisation changes due to alloy impurities only due to intervalley scattering. Specifically, for $L-L$ scattering, the spin-flip scattering strength is on the order of meV, while for 
$\Gamma-L$ transitions, it is an order of magnitude lower.

Using these parameters, we computed the spin relaxation time of GeSn. We found that when sufficient Sn (and strain) is introduced to Ge to induce an indirect-to-direct bandgap transition, the spin relaxation time can increase by several orders of magnitude. At higher temperatures, electron-spin-phonon scattering dominates, and alloy spin-scattering has a minimal effect on the spin relaxation time. In particular, above 50K, the incorporation of $15\%$ Sn (without strain) is enough to significantly improve spin relaxation, while only $10\%$ Sn is necessary below 50K. These results highlight the potential of GeSn as a candidate material for spin-based transistors, quantum computing, and spin interconnects.


% absorption
Finally, in the third part of this project, we calculated the absorption and photoluminescence spectra of GeSn at room temperature and low temperature (75K) in the SWIR light range. Our methods involved the implementation of degenerate and non-degenerate perturbation theory, making this not only the second work to use degenerate perturbation theory in the determination of the optoelectronic properties of a semiconducting material, but also the first ever calculation to introduce the effect of alloy disorder on the indirect and direct transitions. 

We have demonstrated that GeSn alloys exhibit significantly enhanced optoelectronic properties compared to pure Ge. At room temperature, the absorption coefficient of Ge$_{0.88}$Sn$_{0.12}$ approaches $10^5\ $cm$^{-1}$, more than twice that of pure Ge. Furthermore, PL intensity in the SWIR region increases dramatically, with Ge$_{0.88}$Sn$_{0.12}$ exhibiting PL nearly $250$ times stronger than Ge. Perturbation theory proved essential for accurately modelling both the absorption and emission spectra, especially in indirect-gap GeSn. While alloy scattering was found to have a limited impact on the absorption coefficient, it played a central role in shaping the PL response. In indirect-gap GeSn, the PL spectrum is dominated by a peak corresponding to the material’s indirect bandgap, driven primarily by alloy scattering and further influenced by electron-phonon interactions. 

These findings highlight the potential of GeSn as a tunable group-IV material for SWIR optoelectronic applications, and underscore the importance of including both alloy disorder and phonon-assisted processes in theoretical modelling to fully describe its optical behaviour.

The results in this thesis not only highlight GeSn’s suitability for integration into next-generation electronic, spintronic, and photonic devices, but also provide a robust theoretical foundation to guide future experimental validation and device engineering in this rapidly developing field. Our approach in all of our calculations is applicable for a range of semiconductors, particularly group-IV alloys.

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% OUTLOOK GOES HERE
\section{Outlook}


Overall, the findings presented in this thesis provide a more comprehensive understanding of the %optical, transport, and spintronic 
properties of GeSn. However, our work can still be extended in many directions. 

Future research should be able to prove that straining GeSn in the [111]-direction should lead to both a higher electron mobility and a higher spin-relaxation time compared to unstrained GeSn, as this would remove scattering between the L valleys. This could be advantageous for indirect-gap GeSn, where intervalley scattering between the L valleys is dominant.



%For our spin-alloy scattering parameters, group theory can be used to determine which spin-flip transitions are symmetry-allowed. This would require deriving selection rules using the appropriate double group character tables corresponding to the symmetry of each valley in the diamond crystal structure. This would verify our results for both GeSn and SiGe.

% spin relaxation of SiGe...
Our spin-alloy scattering parameters for SiGe could be used to calculate the spin-relaxation time of SiGe using the same approach as in Chapter \ref{chap:spinrel}. This could be crucial for developing spintronic devices that are highly compatible with existing silicon technology, offering better integration than GeSn. Additionally, unlike GeSn, SiGe poses fewer fabrication challenges.

Another promising direction for future work lies in bridging the spin-dependent carrier dynamics studied in Chapter \ref{chap:spinrel} with the optical absorption and emission processes explored in Chapter \ref{chap:Opt}. Specifically, the use of circularly polarised light offers a route to generate spin-polarised carrier populations in GeSn. Using this approach, one could investigate how spin-polarised electrons evolve and recombine in GeSn. Recent experimental research by Rossi et al \cite{rossi2025optical} has already demonstrated spin-to-charge conversion in GeSn by directly injecting optical spin-polarised currents into the alloy. Further studies would enable a deeper understanding of spin-dependent optical transitions, including the potential for circularly polarised photoluminescence, spin-selective absorption, or even spin-lasing in engineered GeSn structures.