## 1 Introduction  
For over a decade, Ge has been actively considered for many nanoelectronic and sensor applications, as it has a number of material property advantages over Si or alternative materials such as silicon-germanium (Si\({}_{1-x}\)Ge\({}_{x}\)) alloys. The main properties include its superior carrier mobilities, low-dopant activation temperatures, and smaller band-gap [1; 2; 3]. A main advantage of Ge-technology is its compatibility to existing Si processes and this may be an important factor as industrial inertia may delay the introduction of more exotic materials, unless, of course, they provide a clear breakthrough as compared to present technologies. The second determining factor for the consideration of Ge is the development of high-\(k\) gate dielectric materials. This, in turn, eliminates the need for a good-quality native oxide for the semiconducting material. The poor quality of germanium dioxide as compared to silicon dioxide in Si-technology plagued Ge-technology in the early days of the semiconductor industry [1]. Defects in semiconductors cannot be avoided in device processing (for example, implantation and diffusion). Essentially, understanding their properties is key to comprehend diffusion and can lead to devices with improved characteristics. For example, diffusion issues are important as the characteristic dimensions of devices are presently only a few nanometers. This necessitates the control of \(p\)- and \(n\)-type dopants to form efficient Ge-based \(p\)- and \(n\)-channel metal oxide semiconductor field effect transistors (MOSFETs) for advanced complementary metal-oxide semiconductors (CMOSs). There have been numerous studies on Ge over the past decade; however, research on Ge was limited for many decades with most being published over the last decade [4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Vacancies (\(V\)) and self-interstitials (\(I\)) are the intrinsic point defects which act as vehicles mediating diffusion and as such understanding of their properties is critical to control the diffusion and/or electrical activation of dopants [26; 27; 28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40]. The dominance of \(V\) is established experimentally [28] and is important as it mediates the diffusion of most dopants in Ge [5; 41; 42]. Concerning donor atom diffusion, previous studies have established that \(n\)-type dopants such as P, As, and Sb diffuse in Ge via a vacancy mechanism at a rate that is faster than self-diffusion [41; 42; 43; 44; 45]. It should be considered that the relatively fast transport of \(n\)-type dopants is not appropriate for the formation of ultra-shallow donor profiles. It is established that \(p\)-type dopants (for example Ga, In, B) diffuse at a lower rate as compared to \(n\)-type dopants [36]. The diffusion of the \(p\)-type dopants is similar to self-diffusion; however, in the case of B, it is significantly lower [46; 47; 48; 49]. This slow diffusion of the \(p\)-type dopants is advantageous for the formation of ultra-shallow and well-defined acceptor doped regions in Ge. The most common isovalent dopant in the Czochralski-grown group IV semiconductors is C [50; 51; 52]. Other dopants such as Sn or lead Pb have been used in defect engineering strategies to contain the fast diffusion of \(n\)-type dopants in Ge [20; 36; 53; 54]. The interest in isovalent doping stems also from the interest to employ group IV binary (for example Si\({}_{1-x}\)Ge\({}_{x}\), Sn\({}_{1-x}\)Ge\({}_{x}\)) and/or ternary (for example Si\({}_{1-x}\)-\({}_{x}\)Ge\({}_{x}\)Sn\({}_{y}\)) alloys in devices [55]. In Czochralski-grown semiconductors such as Ge or Si, there is a non-negligible concentration of oxygen [1; 56; 57; 58; 59; 60]. Oxygen is mainly incorporated in the lattice via the growth process and its impact has been mainly investigated in Si and to a far lesser extend in Ge. Notably, most Ge crystals are pulled in graphite crucibles, leading to a lower oxygen content than in Czochralski-grown Si.