%Alternatively, should i focus my intro on scattering, where Si is low mobility (leads to heat) and a poor light emitter (indirect gap), as well as low SOC. GeSn is an upgrade on all these things.......???????

\chapter{Introduction} \label{chap:intro}

%\section{Background and Motivation}

\section{Energy Consumption in Electronics}


% ideally i would like to update some of this, more modern references
% Data on energy consumption
The rapid advancement of technology over the past few decades has been paralleled by an increasing demand for energy-efficient, high-performance electronic devices. As modern society becomes more dependent on electronics, from consumer gadgets to large-scale data centres, energy consumption has emerged as a critical issue. Currently, the Information and Communication Technology sector is responsible for $\approx 10\%$ of global electricity use, generating $1.4\%$ of greenhouse gas emissions \cite{gelenbe2023electricity,malmodin2024ict}. In Ireland, electricity consumption by data centres has risen from just $5\%$ of the total generated in 2015 to $21\%$ in 2023, according to the Central Statistics Office \cite{cso2024datacentres}. Given the ever-increasing number of electronic devices in daily life, these figures are likely to rise even further. 


% What causes energy consumption
Today, the dominant technology used to build integrated circuits (ICs), including microprocessors, memory chips and other digital logic circuits, is Complementary Metal-Oxide-Semiconductor (CMOS). CMOS uses two types of transistors: NMOS and PMOS (n-type and p-type MOS), which are arranged in pairs to form logic gates. The vast CMOS framework currently offers unparalleled levels of fabrication complexity and high manufacturing volumes and yield. However, CMOS technology is not without its flaws. It relies on charge as the fundamental logic variable, whereby high and low voltage levels represent binary states (0 and 1). Electrons (and thus charge) moving via an electric field is required to switch logic states and transmit information. As electronics have shrunk in size to fit more transistors per area, energy consumption has emerged as a significant bottleneck due to two key factors of power dissipation: 


\begin{enumerate}
    \item \textbf{Dynamic power dissipation:} is largely caused by transistors switching between logic states \cite{romli2015overview}. The NMOS and PMOS transistors remain ON simultaneously for a small period of time, resulting in a direct current path between the power supply and the ground, causing a short-circuit current flow that causes power dissipation in CMOS ICs. Dynamic power is proportional to the square of the supply voltage, the capacitance of the transistors, and the switching frequency. As device dimensions shrink, it becomes harder to reduce supply voltage without compromising performance.
    
    \item \textbf{Static power dissipation:}  this is caused by the transistor not completely turning off. A small amount of current, known as leakage current, still flows due to insufficient insulation. As the number of transistors on a chip increases, the total leakage current increases, leading to power dissipation.    
\end{enumerate}

Both static and dynamic power dissipations have grown exponentially in CMOS processes \cite{romli2015overview}, which has increased device cost and reduced efficiency. Moore's Law \cite{moore1965moore} states that the number of transistors in an IC doubles about every two years, and with current estimates of a billion transistors per chip, dynamic and static power dissipation will be overwhelming and may destroy the device operation \cite{ghising2023graphene}. In addition, the switching of transistors generates heat, which limits the achievable switching rates \cite{sau}.  Given that transistors are such key components of modern electronic devices, it is essential to maximise their efficiency. All of these factors indicate that classical, charge-based logic is reaching its limits, especially in terms of energy efficiency. As we demand more from our electronics, finding an alternative logic variable is one clear avenue in solving this issue.



\section{Electron Spin - A New Logic Variable}

In contrast to traditional electronics, spintronic (spin-transport-electronic) devices take advantage of either both the charge and the intrinsic angular momentum of electrons (known as ``spin") or solely electron spin to store and process information. Spin-based logic operates by changing the spin orientation of electrons (up or down) rather than moving them from one place to another. This additional degree of freedom opens up new possibilities with lower power consumption, since spins can be manipulated with minimal energy using magnetic fields or spin-polarised currents.


Spintronic devices are inherently non-volatile, meaning they retain their state (0 or 1) without the need for continuous power. This eliminates the static power dissipation seen in charge-based devices, where power is required even when the device is idle just to maintain its state. Such non-volatile devices are particularly appealing for reducing standby power consumption in systems like mobile devices or data centres, where idle power accounts for a large portion of total energy usage \cite{biswas2014error}.  Consequently, spintronics holds promise for applications in a range of applications, including data storage \cite{yakout2020spintronics,bandyopadhyay2008introduction}, communication technologies \cite{sanvito2011molecular} and quantum computers \cite{burkard2023semiconductor}. 




\subsection{Spintronic Applications and Devices}

Here, we examine devices that successfully exploit spin, categorising them into the following groups: $(i)$ GMR-based devices (used for memory), $(ii)$ transistors, $(iii)$ light-emitting devices and $(iv)$ quantum applications.


\subsubsection{GMR-based Devices}
 
The discovery of Giant Magnetoresistance (GMR) in 1988 \cite{baibich1988giant,binasch1989enhanced} revolutionised data storage by enabling electron spin manipulation. GMR (Fig. \ref{fig:GMR}) occurs when alternating ferromagnetic and non-magnetic layers exhibit significant changes in electrical resistance depending on the magnetic moments' alignment. This resistance change arises from varying spin-polarised electron scattering rates in parallel versus anti-parallel alignments. 
Numerous spin-based devices have emerged from exploiting GMR. Spin valves \cite{dieny1991giant} consist of two ferromagnetic layers separated by a non-magnetic metallic spacer, while magnetic tunnel junctions (MTJs) replace the non-magnetic metallic spacer with an insulating layer, yielding even greater conductivity differences \cite{chappert2007emergence}. Both MTJs and spin valves are essential components of spintronics devices such as Magnetoresistive Random Access Memory (MRAM), which use spin state changes for information storage \cite{moodera1995large,miyazaki1995giant}, consuming less power than conventional DRAM or flash memory. Also, its non-volatility reduces energy use \cite{singh2019fabrication}. These technologies have enabled high-density storage in hard drives \cite{ghising2023graphene,chappert2007emergence}, with MRAM chips now marketed by multiple companies and GMR’s sensor market impact estimated at $\$$900 million in 2023 according to Global Market Insights Inc. GMR-based read heads are common in laptops, desktops, and phones \cite{bandyopadhyay2008introduction}. The iPod device developed by Apple Inc. is a prime example of a device that utilises GMR \cite{yakout2020spintronics,mccray2009spintronics}.



\begin{figure}[H]
    \centering
    \includegraphics[width=0.65\linewidth]{Background/Figures/GMR.png}
    \caption{A typical GMR structure, where the spacer layer is a non-magnetic material for a spin-valve, or an insulating layer for a MTJ.}
    \label{fig:GMR}
\end{figure}



\subsubsection{Spin-based Transistors}

 A key milestone in spintronics was the 1990 theoretical proposal of the spin field-effect transistor (spin-FET) by Datta and Das \cite{datta1990electronic}, where spin orientations represent “1” and “0” states. A spin-FET comprises two ferromagnetic contacts (source and drain) and a semiconductor (with strong spin-orbit coupling) channel between them (e.g., GeSn or GaAs), as seen in Figure \ref{fig:SFET}. The ferromagnetic materials polarise the electron spins, while a gate terminal controls spin states, akin to traditional FETs. Spin-FETs require minimal energy to flip spins for switching, and operate faster than conventional FETs due to quicker spin manipulation; thus potentially leading to faster devices.  
 
 
 Standard bipolar junction transistors (BJTs) have a p-n-p or n-p-n structure (as in Fig. \ref{fig:SFET}), using both electrons and holes as charge carriers, enabling current amplification when a small input current at the base (middle layer) modulates a larger current between emitter and collector. A spin-BJT (SBJT) is much the same, with the only difference being that the base is ferromagnetic, so the emitter in a SBJT injects spin-polarised electrons into the base. The collector current is influenced by both the spin alignment and charge flow, offering additional control based on electron spin, which could enable lower power consumption and new functionality in electronic devices.


\begin{figure}[H] 
\centering 
    \begin{subfigure}
    \centering 
    \includegraphics[width=0.5\linewidth]{Background/Figures/SpinFET.png} 
    % \label{fig:SFET} 
    \end{subfigure} 
\hfill 
    \begin{subfigure}
    \centering 
    \includegraphics[width=0.48\linewidth]{Background/Figures/SBJT.png}  %\label{fig:BJT} 
    \end{subfigure} 
\caption{Schematic of a spin FET (left), with arrows indicating the magnetisation direction of the source and drain contacts, and an N-P-N Spin Bipolar Junction Transistor (right), with a ferromagnetic base.}  \label{fig:SFET}
\end{figure}




\subsubsection{Opto-spintronics}

Spin manipulation can also be advantageous in optoelectronic devices \cite{vzutic2020spin}. Standard lasers, comprised of an active (gain) region, a resonant cavity and a pump, are solely dependent on electron charge, and have applications in optical storage, printing, medicine, optical sensing, and display systems \cite{chuang1996physics,coldren2012diode,yariv1997optical}. However, spin-polarised lasers (Fig. \ref{fig:spinlaser}), whose main distinction is the spin-polarisation of its electrons in the active region, are expected to outperform standard lasers. Only electrons are considered as spin carriers since the spins of holes decay much faster \cite{vzutic2004spintronics}. Spin-polarised carriers can be achieved either through the use of two magnetic contacts (as per Fig. \ref{fig:spinlaser}) or via optical injection using circularly polarised light. Electrons and holes recombine in the gain region, and depending on the spin orientation of the electrons, the resulting photons emitted will have either right- or left-handed circular polarisation. Transferring spin-polarised electrons to circularly polarised photons in this way results in spin-encoded signal travelling much faster and further \cite{vzutic2020spin}, offering new avenues of information transfer. Spin-dependent effects such as ultrafast optical switching \cite{wang2024all,hopfner2014controlled,hallstein1997manifestation}, polarisation control \cite{nan2020controlling,younis2024spin,ando1998photon} and threshold current reduction \cite{lee2014spin,rudolph2003laser} have been demonstrated using circularly polarised photo-excitation to generate spin-polarised carriers. The ability to independently control optical polarisation and intensity in spin-polarised lasers make them applicable in reconfigurable optical interconnects, chiroptical spectroscopy, and high-bandwidth telecommunications \cite{holub2007electrical}. Despite significant research progress, opto-spintronic devices have not yet transitioned to commercial products.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.75\linewidth]{Background/Figures/spinlaser.png}
    \caption{Schematic of a spin-laser, where the resonant cavity is formed by two mirrors made of distributed Bragg reflectors (DBRs) and the active region is typically composed of quantum wells/dots. The upper spacer is p-type while the lower spacer is n-type.}
    \label{fig:spinlaser}
\end{figure}





\subsubsection{Quantum Devices}

Leveraging quantum mechanical principles such as superposition and entanglement to process information, quantum computing may help solve problems which are beyond the means of classical computers. Unlike classical bits (0s and 1s), quantum bits (qubits) can exist in multiple states simultaneously (superposition) and interact via entanglement, enabling exponentially scalable computations. Spin-based quantum computing, a leading approach for scalable quantum systems, uses semiconductor quantum dots to trap charges and spins, with smaller dots used to create qubits and larger ones for applications in sensors. The spin of a single electron can encode one qubit. Spin qubits have been demonstrated in materials such as GaAs \cite{dots5coherent,bluhm2011dephasing}, Si \cite{wang2011collective}, Ge \cite{watzinger2018germanium}, and graphene \cite{trauzettel2007spin}. Intel has developed advanced silicon spin qubit quantum computers \cite{boerkamp2023intel,moore2020intel}. 

To enable communication between spatially separated qubits, spin buses (or quantum buses), coherent channels for transferring quantum information via spin interactions, are being explored as a key component for scalable architectures. These buses facilitate long-range entanglement and qubit connectivity, overcoming the limitations of local interactions in densely packed qubit arrays. Fig. \ref{fig:qubus}, taken from Ref. \cite{langrock2023blueprint}, provides a detailed schematic of a quantum bus, whereby a quantum dot, which carries a single electron, is formed within a quantum well by multi-layer metallic surface gates, and is shuttled across a 1-D channel. The electron and its spin state are detected by transistor gates at the ends of the quantum bus.

\begin{figure}[H]
    \centering
    \includegraphics[width=0.95\linewidth]{Background/Figures/qubus.png}
    \caption{Schematic cross section of a quantum bus device.}
    \label{fig:qubus}
\end{figure}


\subsection{Challenges - Finding a Candidate Material}

% Challenges - more detail??
Despite its obvious potential, spintronics faces numerous challenges, such as the generation of fully polarised carriers, injection of spin into devices, long-distance spin transfers and the manipulation and detection of the spin orientation of carriers \cite{li2016first}. Solving these issues requires two things: the development of device fabrication and the design of new materials with properties suitable for spintronics. Focusing on the latter, the advancement of spintronics has been significantly driven by the development of materials that can efficiently manipulate electron spin. Materials whose electron spins can be injected, manipulated and detected can broadly be categorised into magnetic materials, topological insulators (TIs) and non-magnetic semiconductors. TIs such as HgTe \cite{konig2007xiao} and Bi$_{1-x}$Sb$_x$ \cite{hsieh2008topological} are insulators in bulk, but metallic on their surface, and are ideal for spin generation and transport. However, to this day, they can only operate at low temperatures \cite{islam2019low}, and are yet to be used in practical applications.


% magnetic materials - ferro/ferri
Magnetic materials can be either spontaneously or non-spontaneously magnetic; that is, spontaneous magnetism occurs even in the absence of an externally applied magnetic field \cite{simon2013oxford}. Spontaneous magnetism can occur in the form of ferromagnetism (where adjacent electron spins are aligned), anti-ferromagnetism (where adjacent electron spins are anti-aligned) or ferrimagnetism (where adjacent electron spins are anti-aligned, but the magnitudes of these opposing moments are unequal, resulting in a net magnetic moment). All three forms of spontaneous magnetism comes with advantages and disadvantages when it comes to their application in spintronics. 


% magnetic materials - ferro
Ferromagnetic materials (such as iron, cobalt, and nickel) serve as spin injectors and detectors in devices such as MTJs and spin valves. However, ferromagnets produce stray magnetic fields which can cause cross-talk between individual components on small length scales, an issue which will only increase as we move towards smaller scale devices. Additionally,
ferromagnetics can only supply partially spin-polarised carriers due to their low degree of spin polarisation \cite{li2016first}. 


% magnetic materials - ferri
Antiferromagnets (like CuMnAs) and ferrimagnets (such as GdFeCo) exhibit a much faster switching speed than ferromagnets \cite{fiebig2008ultrafast}. Antiferromagnets possess a range of spin-related phenomena such as spin polarisation \cite{vsmejkal2020crystal} and the magnetic spin Hall effect \cite{zhang2018spin,vzelezny2017spin}. However, they are complex in their behaviour and are by no means fully understood \cite{li2016first}. In addition, the partially cancelled magnetic moments in ferrimagnets mean that they generally exhibit lower net spin polarisation, which can reduce efficiency in some spintronic applications. Furthermore, (anti-)ferromagnets and ferrimagnets have a Curie temperature and can lose their magnetic properties at higher temperatures.


% magnetic materials -para/semi
Regarding materials with non-spontaneous magnetism, paramagnetic materials (due to their unpaired electrons) can align weakly with an external magnetic field, but this alignment disappears when the field is removed. They find limited applications in spintronics since they do not retain magnetisation and thus cannot sustain spin polarisation over time. Interestingly, semiconductors can be made to be ferromagnetic through doping with magnetic ions. Magnetic semiconductors (such as GaMnAs and InMnAs) are of interest due to their easy implementation into devices utilising current semiconductor technology. However, most magnetic semiconductors suffer from low magnetic ordering temperatures, which limits their use in practical applications \cite{li2016first}.




% Materials - semiconductors
The ideal candidate material could be a non-magnetic semiconductor such as silicon (Si), germanium (Ge), or germanium-tin (GeSn), which exhibits sufficient spin properties such as spin-orbit coupling. Non-magnetic semiconducting materials have emerged as critical to spintronics due to their ability to support both spin and charge transport, allowing for controlled manipulation of spin currents (typically via spin injection), spin transport, and spin detection whilst being seamlessly implemented into modern-day processing and fabrication technologies, bridging spin-based technology and traditional electronics.



% Conclusion
To summarise, ``spin currents" have the potential to replace conventional charge currents for transfer and storage of information, allowing for faster, low-energy operations \cite{chappert2007emergence}, in particular through group-IV materials Si, Ge and Sn.  In the next section, we will examine these group-IV materials in more detail, ultimately proposing GeSn as a promising semiconductor for future applications, not only in spintronics but also in optoelectronics and transport.







\section{GeSn - A New Semiconductor}

% - Si
CMOS technology is built on silicon, with over $99\%$ of all semiconductor devices fabricated on Si \cite{nekrashevich2014electronic}. Si has been the foundation of the semiconductor industry for over 50 years for a variety of reasons. It is one of the most abundant elements on earth, and it's low bandgap of $1.1eV$ \cite{zanatta2019revisiting,pankove1972optical} makes it an ideal semiconducting material; effective for switching devices. Si offers excellent thermal resilience, operating reliably at temperatures ranging from $-40$ to $125 \ ^o C$ (with relatively low current leakage), allowing its use in diverse environments, from auto-mobile electronics to consumer laptops and smartphones. One of the most important properties of Si is that it forms a stable and high-quality native oxide layer (SiO$_2$) when exposed to oxygen. SiO$_2$ acts as an excellent insulator, which allows for precise control over the behaviour of transistors, specifically metal-oxide-semiconductor field-effect transistors (MOSFETs) \cite{nekrashevich2014electronic}. In the context of spintronics, Si possesses relatively long-lived electron spins \cite{morton2011embracing,li2011spin}. Spin information in Si can be transported over hundreds of microns \cite{huang2008geometric,qing2015spin}, which is compatible with on-chip interconnect length scales \cite{chalaev2017suppressing,dery2011silicon,vzutic2011taming}. Advancements in injecting spin-polarised current into Si \cite{spiesser2017giant,dankert2013efficient,appelbaum2007electronic,jonker2007electrical,grenet2009spin,dash2009electrical} indicate the potential for incorporating semiconductor spintronic device concepts into hybrid Si architectures \cite{tang2012electron}. 



% Si limitations 
However, as we continue to push towards further miniaturisation and higher performance, Si is approaching its physical and operational limits \cite{flack2016gan}. While Si has long dominated digital logic applications, its properties are less suited for analog high-frequency electronics and optoelectronics. One key limitation is its relatively low electron and hole mobility compared to other group-IV (and most III-V) semiconductors. This causes charge carriers to move more slowly, directly affecting the switching speed of transistors and leading to slower device operation overall. A significant factor contributing to Si's low electron mobility is its indirect bandgap, which limits its effectiveness in many applications. In optoelectronics, Si's indirect bandgap makes it poorly suited for use in light-emitting devices. As a result, Si-based light emitters are not viable options in this field, with III-V materials preferred. Since III–V materials lack both lattice compatibility with silicon and CMOS-process compatibility, research has focused on developing materials that not only provide optimal optoelectronic properties but also integrate seamlessly onto the Si platform. Finding a suitable candidate material would allow electrical and optical processing to coexist on the same chip, improving performance, reducing power consumption, and lowering costs. Silicon can be turned into a photonic material via nanostructuring \cite{bettotti2002siliconnanostructures}, with recent evidence \cite{priolo2014silicon} suggests that some Si nanostructures exceed the performance of equivalent direct-bandgap materials. While nanowire arrays are extremely strong absorbers, with around $95\%$ of solar panels build using Si (according to the US Department of Energy), no light-emitting devices based on Si nanocrystals have reached the market. 
%One of the outstanding goals of photonics is to produce a material than can provide optimal optoelectronic properties and simultaneously integrate seamlessly onto a Si platform. III-V materials lack both the lattice and CMOS-process compatibility to achieve such a goal. 





% Alternatives - GeSn
Several alternative high-mobility semiconducting materials have been proposed to replace Si, including III-Vs \cite{del2011nanometre}, graphene \cite{schwierz2010graphene}, transition metal dichalogenides (TMDs) \cite{fiori2014electronics} and most notably, Ge (and its alloys) \cite{pillarisetty2011academic,schulte2017fabrication}. Among these alternatives, Ge and its alloys are the most promising candidates to replace Si in CMOS technology, owing to their excellent compatibility with Si processing. Like Si, Ge has a diamond face-centred cubic (FCC) crystal structure - two interpenetrating FCC primitive lattices, as shown in Figure \ref{fig:fcc} (taken from Ref. \cite{weerasinghe2006electrical}). Although its abundance is significantly lower than Si, Ge has the benefit of a higher carrier mobility than Si (n-type (x3), p-type (x4)). Despite this advantage, Ge also has an indirect bandgap, making it a poor light emitter. Sufficient biaxial tensile strain can cause an indirect-to-direct bandgap transition in Ge, although the amount of strain required causes the material to approach critical thickness. 


\begin{figure}[h]
    \centering
    \includegraphics[width=0.4\columnwidth]{Background/Figures/diamondfcc.png}
    \caption{Diamond FCC crystallographic structure; the structure for Group IV materials Si, Ge and Sn.}
    \label{fig:fcc}
\end{figure}



% https://pubs.aip.org/aip/apl/article/118/11/110502/39502 (nice link on GeSn)
% GeSn - direct gap

 Crucially however, introducing sufficient Sn to Ge also induces a direct gap in the material. Sn is a semi-metal (which by definition has a zero direct gap) that can be found in two phases: high-temperature metallic $\beta$-Sn and the low temperature semi-metallic $\alpha$-Sn, with a thermodynamic phase transition of $13.2^\circ C$. When referring to GeSn, $\alpha$-Sn is the phase of reference since it also has a diamond FCC crystal structure. Therefore, Ge and Sn can be mixed in a solid solution to obtain a semiconductor (for high-Ge content) or semi-metal (for high Sn content), with the same diamond FCC crystal structure of the two elemental materials. In semiconductor physics, the focus is on high-Ge GeSn, and this will be the basis of this work. The lattice parameter of GeSn varies linearly with composition between the lattice constants ($a_0$) of Ge and Sn, as per Vegard’s law \cite{polak2017electronic,xu2017deviations,magalhaes2022confronting}. The lattice mismatch between Ge and Sn is quite large ($14.7\%$), and later in this chapter we shall discuss the consequences of this mismatch when using GeSn in processing. In $1982$, based on the alloying properties governed by Vegard's Law, 
 Goodman \cite{goodman1982direct} proposed GeSn as a direct-gap semiconductor. A few years later, theoretical studies supported these observations, with Jenkins et al. \cite{jenkins1987electronic} predicting a direct gap at $20\%$ Sn concentration using the virtual crystal approximation (VCA). In 2007, Moontragoon et al. \cite{moontragoon2007band} exploited supercell mixing to predict the indirect to direct transition at $17\%$ Sn, while a year later Yin et al. \cite{yin2008origin} used density functional theory (DFT) to predict the transition at $6.3\%$ Sn. Today, the indirect-to-direct bandgap transition of GeSn is generally accepted to be in the range of $7-9\%$ Sn concentration \cite{jiang,ghetmiri2014direct,gallagher2014compositional}.



There are several reasons why GeSn has become increasingly desirable for applications in the semiconductor industry. Its pseudo-direct and direct bandgap characteristics (discussed in detail in Chapter \ref{chap:gesn}) have driven significant research interest in exploring its transport and optoelectronic properties (especially in the short-wavelength, mid-wavelength and near-infrared range \cite{moutanabbir2021monolithic}). In addition, GeSn is also a likely candidate for spin-based devices. These factors, along with its compatibility with existing silicon-based semiconductor manufacturing processes is what makes GeSn a hot-topic material. Within this section, we explore much of the recent academic work on GeSn that has led to its proposed use in a wide range of devices.





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\bigskip
%\newpage
\subsection{Applications of GeSn}



\subsubsection{Transport Applications}

% The commented paragraph below explains polar bonds well!!
%The bonding between group-IV atoms is covalent, meaning the electrons are shared relatively equally between the atoms. Covalent bonds do not produce strong electric dipoles because the electronegativity difference between the atoms is small or negligible. Therefore, when the crystal lattice vibrates (through phonons), it does not generate significant internal electric fields. In contrast, III-V and II-VI compounds are bonded by polar bonds, where the difference in electronegativity is large, leading to the formation of dipoles within the crystal. The absence of polar bonds led to GeSn being proposed as a high-mobility material, due to the absence of polar-optical-phonon scattering; typical in III-V and II-VI compounds \cite{giunto2023gesn}.

GeSn was initially proposed as a high-mobility material due to the absence of polar-optical-phonon scattering; typical in III-V and II-VI compounds \cite{giunto2023gesn}. In general, direct gap semiconductors with diamond and zincblende structure have a higher mobility than those with an indirect-gap. Ge has a high room-temperature electron mobility ($3900\ cm^2/(Vs)$ \cite{Fisch,prince}) compared to Si ($1400\ cm^2/(Vs)$ \cite{ludwig1956drift}). Upon sufficient introduction of Sn to Ge to induce an indirect-to-direct bandgap transition, a substantial increase in the electron mobility can be expected \cite{sau,mukh}. Recent experimental findings from Tien et al \cite{mobvt2021} show an increase in the mobility of tensile strained n-GeSn with increased Sn content and strain, and decreased temperature. Additionally, Ge has a higher room-temperature hole mobility ($1900\ cm^2/(Vs)$) than Si ($450\ cm^2/(Vs)$)  \cite{sze2021physics}. Strained Ge has been proposed as a high hole-mobility material, which have resulted in record-high 2D hole gas mobilities in strained-Ge QW modulation-doped heterostructures \cite{scappucci2021germanium,melnikov2015ultra}. Moreover, Myronov et al \cite{myronov2023holes} have measured a record-high hole mobility of $4.3 \times 10^6 \ cm^2/(Vs)$ in strained Ge at $300mK$. %This has fuelled the development of quantum-electronic circuits based on spin-qubits. 



% transistors
High-mobility materials improve transistor speed and efficiency, prompting significant work on GeSn transistors. In 2011, Gupta et al \cite{gupta2011gesn} developed the first p-MOSFET on Ge$_{0.97}$Sn$_{0.03}$, which showed up to $20\%$ improvement in hole mobility over bulk Ge. Later, Huang et al \cite{huang2017high} demonstrated a compressively strained $Ge_{0.9}Sn_{0.1}$ quantum-well p-MOSFET with a hole mobility of $509\ cm^2/(Vs)$. Liu et al \cite{liu2021high} achieved an electron mobility of $700\ cm^2/(Vs)$ in tensile-strained Ge$_{0.96}$Sn$_{0.04}$ n-MOSFETs and a record-low contact resistivity of $1.5\times 10^{-7}\Omega \ cm^2$. GeSn also shows potential for tunnel field-effect transistors \cite{hu2008green,sant2014pseudopotential}.

% In physics, kappa (κ) is often used to denote the dielectric coefficient, a measure of how easily a material can be polarized by an electric field. 



\subsubsection{Optoelectronic Applications} 

% Intro 
Radiative recombination in indirect-gap semiconductors is slower and weaker than in direct-gap materials since it can only occur through the absorption or emission of phonons \cite{peter2010fundamentals}. Consequently, direct-gap GeSn is a strong candidate for a range of optoelectronic applications.


% Photodetectors
Photodetectors (PDs) convert optical signals (light) into electrical signals (current or voltage), and are key components in cameras, solar cells, fibre-optic communication, and various scientific instruments. GeSn photodetectors extend operation to longer wavelengths compared to pure Ge, due to bandgap engineering. Si-based GeSn PDs have been developed for mid- and short-wave infrared applications \cite{tran2019si,zhang2018gesn}. Recent advances include high-broadband GeSn photodiodes for extended-SWIR applications \cite{atalla2022high} and CMOS-compatible dual-band detectors \cite{talamas2021cmos}. 

 

% LEDS
% https://www.nature.com/articles/s41598-024-60686-3   This link tells the story of the development of the GeSn laser really well.
% Lasers - I want to reduce
The direct bandgap in GeSn enables its use in light-emitting diodes (LEDs) and lasers, traditionally dominated by III-Vs. GeSn has been demonstrated in LEDs initially at $5\%$ \cite{chang2017room} and $15\%$ \cite{cardoux2022room} Sn concentration. Also, Huang et al. \cite{huang2019electrically} demonstrated the first electrically injected GeSn vertical-cavity surface emitter on the Si-on-insulator platform. The demonstration of optically pumped lasing in direct bandgap GeSn (at $90K$) in 2015 by Wirths et al \cite{wirths2015lasing} initiated the expansion of research in this field. 
Optically pumped GeSn lasers were demonstrated at temperatures progressively approaching room-temperature \cite{zhou2019optically,elbaz2020ultra}, with the first electrically pumped laser demonstrated in 2020 at cryogenic temperatures \cite{zhou2020electrically}. Since then, significant improvements in the performance of GeSn-based have been achieved \cite{kim2022improved,ojo2022silicon,marzban2022strain}. In a recent study, Chen et al  \cite{chen2024tensile} have achieved a tensile-strained GeSn microbridge lasers with a tuneable wavelength, whereby the application of strain reduced the laser threshold by almost $70\%$. Significantly, Buca et al \cite{buca2022room} achieved room-temperature lasing in Ge$_{0.86}$Sn$_{0.14}$ microdisks, showing that the inclusion of biaxial tensile strain enabled laser emission up to $300 K$, compared to $265 K$ for unstrained microdisks.

% tuneable wavelength of over 45nm..


% The rest (largely optical interconnects, which are communication systems that use light to transmit data between different parts of a system)
GeSn has also been demonstrated in optical interconnects \cite{miller2009device,liu2018chip}, lab-on-chip trace gas detection \cite{lavchiev2016photonics}, and monolithic Si photonics for near-infrared and short-wave infrared wavelengths \cite{moutanabbir2021monolithic,giunto2023gesn,dutt,liu2007tensile,wirths2013tensely}. GeSn waveguides exhibit optical gain at room temperature \cite{li2022room}, and has also shown promise for multi-junction solar cells \cite{conley2012high}.

For a more in-depth review on the potential influence of GeSn in optoelectronics, we recommend reading the review article on ``Defects in Ge and GeSn and their impact on optoelectronic properties" by Giunto and Fontcuberta i Morral \cite{giunto2024defects}.





\subsubsection{Integration with Si-technologies}

As we've discussed, since virtually all processing units are based on Si-CMOS fabrication, integrating photonic components within this established technology is highly advantageous \cite{hu2017silicon}. However, the inherent limitations of Si as a light emitter highlight the need for alternative materials that can seamlessly integrate with existing CMOS chipsets. From a growth and processing perspective, GeSn seems the most logical choice. With its direct bandgap and ability to be grown directly on Si substrates \cite{gesn1997}, GeSn presents a unique opportunity to bring both light-emitting and detecting functionalities onto Si chips, enabling a fully integrated CMOS-compatible optoelectronic platform. GeSn has already demonstrated promise in multiple aspects of Si photonics, paving the way for the direct integration of light sources into Si-based circuits.

Integrating group-IV-based light sources on Si substrates has been an active area of research for decades but has yet to achieve significant technological impact. This has largely been due to challenges in material synthesis and the methods used to demonstrate these light sources on Si. However, recent advancements in group-IV-based light source development \cite{zhou2019optically,elbaz2020ultra,chow2012model,stange2016optically,al2016optically,singh2014mid,von2015direct,fadaly2020direct} suggest that these technologies could soon play a transformative role in optoelectronics \cite{hudait2021design}.




\subsubsection{Spintronic Applications}

Spintronic devices usually require materials with long spin relaxation times (explained in Chapter \ref{chap:spin}) which, in non-magnetic semiconducting materials, depend on the atomic number of the constituent atoms. Ge, with its higher atomic number ($32$) compared to Si ($14$), exhibits stronger spin-momentum interactions \cite{giorgioni2016strong,giorgioni2014valley}, making it a promising candidate for spin-to-charge conversion \cite{dushenko2014spin,dushenko2015experimental,oyarzun2016evidence,bottegoni2017spin} and a likely candidate material in spintronics applications \cite{hoffmann2015opportunities,de2019spin}. Spin-relaxation times in Ge lie in the nanosecond range, with typical spin-diffusion lengths of micrometers \cite{hamaya2018spin,marchionni2021inverse,zucchetti2019doping}. 


Cesari et al. \cite{de2019spin} demonstrated nanosecond carrier lifetimes in Ge$_{0.95}$Sn$_{0.05}$ under compressive strain at $300K$, marking the first optical generation of net spin polarisation in GeSn.  They hypothesised that $\alpha$-Sn, which is a heavy Group-IV element with atomic number $50$, could further enrich the spin-dependent phenomena observed in Ge. Subsequent studies revealed GeSn's enhanced spin-Hall effect and spin-to-charge conversion efficiency, over ten times that of Ge \cite{marchionni2021inverse}. This enables spin lasers and quantum phase control via strain and electric fields \cite{liu2021high,ferrari2023quantum}. More recently, Longo et al \cite{longospin} investigated spin pumping in strained GeSn, which was shown to be governed by the spin-flip relaxation times induced by alloying effects. This represented the first step towards the investigation of spin-to-charge conversion properties in GeSn thin films. GeSn also supports spin current injection and manipulation, as shown by Fettu et al. \cite{fettu2023mid}, who demonstrated increased spin polarisation with Sn content. They concluded that GeSn can be exploited to achieve quantum coherent manipulation and ultimately lead to quantum sensing. Moreover, Liu et al \cite{liu2021high} succeeded in controlling spin orientations via electric fields (top gating) in GeSn/Ge heterostructures. Additional research on phase-coherent transport \cite{weisshaupt2020weak,kaul2024phase}, angular negative magneto-resistance \cite{shu2021negative} and 2D hole gas conduction \cite{tai2021strain} indicate the potential of GeSn in spintronics. 



%\bigskip
% The below is encompassed in the shorter paragraph above

%Further spin-coherent dynamics measurements were carried out by Marchionni et al \cite{marchionni2021inverse}, who investigated the photo-induced inverse spin-Hall effect in Ge$_{0.95}$Sn$_{0.05}$. They extracted a spin-Hall angle in GeSn over ten times larger than that of Ge, resulting in a  spin-to-charge conversion efficiency at least ten times larger than the one of Ge, thus enabling the possibility of effective spin lasers. This research was furthered by Ferrari et al \cite{ferrari2023quantum}, who disclosed the quantum spin Hall phase in GeSn/Si heterostructures. Their work accommodated the existence of gate-controlled chiral edge states; a platform which permits strain and electric field control of the spin-orbit interaction, enabling quantum phase transitions in Si-based devices. Liu et al \cite{liu2021high} also succeeded in controlling spin orientations via electric fields (top gating) in GeSn/Ge heterostructures. Most recently, Longo et al \cite{longospin} investigated spin pumping in strained GeSn, which was shown to be governed by the spin-flip relaxation times induced by alloying effects. This represented the first step towards the investigation of spin-to-charge conversion properties in GeSn thin films.
%}



The strong spin properties effects of GeSn make it an ideal candidate for spin-based devices such as spin-FETs \cite{chuang2015all}, spin qubits \cite{liu2021high,hendrickx2020fast} and spin interconnects \cite{dery2011silicon,vzutic2019proximitized}, which can be used in quantum computing, communication and simulation. The use of GeSn in spintronics applications like ultrafast optical switches, which demand short spin lifetimes, can be achieved through careful tuning of the alloy and dopant concentration. Given that the carrier lifetime of GeSn can be engineered by alloy content, strain and temperature, GeSn offers a versatile platform for the integrated implementation of spintronic architectures \cite{marchionni2021inverse}. Nevertheless, it is clear that despite its promising potential, research on GeSn alloys, particularly in spintronics, remains in its early stages.





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Experimental Challenges}

Currently, despite over 15 years of extensive research, there are no GeSn-based commercial devices. There are several experimental challenges associated with GeSn which has hindered its rise in electronics. The solubility of Sn in Ge is low due to the large lattice mismatch \cite{ayan2019strain,thurmond1953equilibrium}, restricted to $1.1\%$ at $400^\circ C$ \cite{momma2011vesta}, and is below $1\%$ at room temperature \cite{olesinski1985bulletin},  as we see in Figure \ref{fig:phase} (taken from Ref. \cite{olesinski1985bulletin}). Sn will segregate out of the Ge crystal without out-of-equilibrium processing, resulting in the formation of $\beta$-Sn, which is damaging for opto-electronic devices. Therefore, phase-separation during growth or post-growth thermal processing is problematic. This segregation is kinetically hindered by the low atomic diffusivity at room temperature. However, Sn atoms may acquire sufficient thermal energy to segregate to the material's surface or cluster in the bulk into $\beta$-Sn via thermal processing of the material (through doping, annealing or any heat-based CMOS post-growth process) \cite{li2013strain,von2020thermally}. Sn segregation can also occur if the substrate temperatures are too elevated \cite{wu2020insights}. It is therefore necessary to prevent Sn segregation by preserving a low thermal budget throughout growth processes. An excellent review of Sn segregation and thermal instability in GeSn can be found in the paper by Giunto et al. \cite{giunto2023gesn}.
 

\bigskip

% Include phase diagram
\begin{figure}[H]
    \centering
    \includegraphics[width=0.8\linewidth]{Background/Figures/Phase.PNG}
    \caption{Phase Diagram of GeSn under equilibrium conditions.}
    \label{fig:phase}
\end{figure}

\bigskip
% epitaxial relaxation next
Issues with the material performance of GeSn also arise from its inability to grow on a suitable substrate without relaxation defects. GeSn is best integrated into devices in a monocrystalline structure in order to avoid the formation of grain boundaries, which would introduce trap states (states within the bandgap where electrons or holes can become trapped). This would increase electron and hole scattering and prove detrimental to carrier transport. To produce monocrystalline GeSn, the alloy must be grown on a substrate with a suitable crystal structure and lattice parameter \cite{giunto2023gesn}. The closest material to fit (structurally) this criterion is silicon. However, the lattice mismatch causes strain relaxation via dislocations. This problem can be partially alleviated by growing GeSn on Ge-buffered Si(100) substrates or on Ge substrates \cite{people1985calculation}, leading to a much higher critical thickness for strain relaxation. Epitaxial relaxation defects need to be managed correctly to maximise optoelectronic device performance. Despite these challenges, there has been success in growing GeSn alloys in recent years. In particular, Diao et al \cite{diao2025magnetron} have grown GeSn films with Sn content exceeding $25\%$ on InP substrates using a magnetron sputtering growth mechanism. Additionally, Assali et al \cite{assali2019enhanced} implemented a multi-layer GeSn heterostructure to facilitate the incorporation of Sn up to $18\%$ in the top layer. while Schwarz et al \cite{schwarz2020alloy} utilised molecular beam epitaxy (MBE) to grow GeSn on Ge with Sn concentrations of up to $17\%$. Results such as these give hope to GeSn being used on an industrial level.

%There has been success in growing GeSn alloys in recent years. Perhaps most significantly, using a reduced pressure chemical vapour deposition (RPCVD) growth tool, Kong et al \cite{kong2022growth} succeeded in growing high-quality GeSn alloys with high Sn content (up to $18\%$) using $SnCl_4$ and $GeH_4$ precursors at temperatures ($285$-$320^\circ C$) by examining lateral etching of Ge buffers on Si wafers, as well as vertical etching on $Ge/GeSnOI$ (oxide-bonded) wafers. They calculated the Sn concentration using lattice mismatch parameters provided by X-ray analysis. This gives hope to GeSn being used on an industrial level.


%\bigskip

%In general, advances in non-equilibrium growth techniques such as molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) have enabled the fabrication of GeSn alloys with much higher Sn concentrations. In addition, the Sn concentration required for a direct-gap material can be reduced with the application of biaxial tensile strain \cite{gupta2013achieving}, as we will show in Chapter \ref{chap:gesn}. As a result, GeSn remains an alloy of strong interest in condensed matter physics. Since GeSn is of interest largely due to its direct-gap nature at sufficient Sn concentration, coupled with the experimental issues of introducing Sn to Ge, the combination of adding biaxial tensile strain and Sn to Ge could be the most experimentally suitable way to achieve a direct gap in GeSn. }
%In order to strain GeSn in such a manner, one would require a substrate with a large lattice constant. In Figure \ref{fig:bandvstrain}, we can see the direct and indirect gaps of GeSn against the lattice constant of GeSn. This can indicate the lattice constant lower bound a substrate must have in order to strain GeSn sufficiently. % I need to phrase this better.
%}
% Also want to discuss possible substrates which would tensilely strain GeSn. Should I suggest materials? InSb, GaSb, InAs

%\bigskip

%\begin{figure}[H]
%    \centering
%    \includegraphics[width=0.65\linewidth]{Background/Figures/Bands_v_strain.png}
%    \caption{Energy (eV) of the $\Gamma$ (red) and $L$ (black) valleys of GeSn against lattice constant $\AA$.}
%    \label{fig:bandvstrain}
%\end{figure}


In summary, the growing energy consumption in semiconductor manufacturing and the limitations of CMOS processes, particularly due to silicon’s indirect bandgap and low carrier mobility, underscore the need for alternative materials and logic variables. Electron spin offers a promising alternative logic variable for more energy-efficient computing. Additionally, GeSn has emerged as a potential semiconductor material for next-generation technologies due to its higher mobility and potential for integration in spintronics, transport, and optoelectronics. These advances could overcome silicon’s limitations and play a crucial role in the development of more efficient and versatile electronic devices. To emphasise its growing intrigue, Figure \ref{fig:gesnpub} shows the increasing number of publications on GeSn over the last 20 years, according to data found on Ref. \cite{burnham2006scopus}.


\bigskip

\begin{figure}[H]
    \centering
    \includegraphics[width=\linewidth]{Background/Figures/GeSn_Publications.png}
    \caption{GeSn manuscript evolution in the scientific community in the past 20 years (2004-2024).}
    \label{fig:gesnpub}
\end{figure}
% Update this graph before submission
% Go to scopus.com , type in GeSn, go to "analyze results" up in the top right


% https://pubs.aip.org/aip/apl/article/118/11/110502/39502 (nice link on GeSn)








\newpage
\bigskip
\section{Thesis Overview}

The remainder of this thesis is outlined as follows:

\begin{itemize}
    \item Chapter \ref{chap:spin} presents a literature review of electron spin, from its theoretical discovery and role in quantum mechanics to modern relaxation mechanisms. We focus primarily on the Elliott-Yafet (EY) mechanism and developments made to it since its proposal in the 1950s.
    
    
    \item In Chapter \ref{chap:theory}, we review the theoretical methods used in calculating the band structure of GeSn; in particular, Density Functional Theory (DFT), the local density approximation (LDA), plane-waves, pseudopotentials, the GW approximation, \textbf{k.p} theory and the Kane model.

    \item In Chapter \ref{chap:gesn}, we give a detailed description of the band structure properties of GeSn, with a particular emphasis on achieving a direct-gap material, which directly impacts its suitability for transport, spintronic and optoelectronic applications. 

        
    \item We treat general scattering theory in Chapter \ref{chap:theory2}, using the T-matrix formalism to derive an expression for elastic alloy scattering for a disordered binary alloy. This is done using a supercell approach, whereby a single impurity is substituted into a periodic host lattice. We discuss the frozen phonon method in deriving phonon-parameters crucial to electron-phonon scattering. We also produce an expression for the carrier mobility using the relaxation time approximation and the Boltzmann Transport Equation. Finally, we implement degenerate and non-degenerate perturbation theory to derive an expression for calculating the absorption coefficient and photoluminescence spectrum for indirect and direct transitions.
    
    \item In Chapter \ref{chap:trans}, we calculate the intra- and inter-valley electron-alloy scattering parameters in n-type GeSn alloys. These parameters are used to determine the alloy scattering contributions to the n-type electron mobility of GeSn at $300K$ and $15K$ using a first iteration of the Boltzmann transport equation in the relaxation time approximation. Mobility is calculated as a function of Sn concentration, biaxial tensile strain and temperature. Our findings suggest that GeSn has potential applications as a high mobility 2D electron gas.
    
    \item In Chapter \ref{chap:spinrel}, we develop the first-principles methods used in Chapter \ref{chap:trans} to calculate the spin-alloy scattering parameters of GeSn. We use these parameters along with electron spin-phonon parameters to calculate the spin relaxation time of GeSn as a function of Sn concentration, temperature and strain. The strong spin-orbit properties tunable bandgap nature of GeSn mean its relaxation time can change by several orders of magnitude, leading to its potential in a range of spintronic applications.

    \item Chapter \ref{chap:Opt} presents room-temperature and low-temperature (75K) absorption and emission spectra of GeSn alloys, with a focus on the short-wave infrared light range. The results highlight how small additions in Sn content significantly enhance the material's optoelectronic properties. These findings support the potential of GeSn as a group-IV alternative to III–V semiconductors for CMOS-compatible photonic integration.

    \item Finally, a summary of conclusions and an outlook of future topics of research are presented in Chapter \ref{chap:conc}.
\end{itemize}


This work has led to publications listed in references \cite{myronov2023holes}, \cite{sewell2025first} and \cite{sewell2024controlling}, including a pre-print submission in Ref. \cite{sewell2025spin}.