# Seventy-Five Years since the Point-Contact Transistor: Germanium Revisited
## 4 Defect Processes in Ge
### Donor Atoms  
The technologically important donor atoms (D) in Ge are phosporous (P), arsenic (As) and antimony (Sb). As indicated above, the prevalent intrinsic point defect in Ge is the vacancy. These occupy substitutional positions in the Ge lattice and, as they can be easily ionised at room temperature, they readily offer an electron to Ge, thus increasing its conductivity. What is left behind is a positively charged dopant that can attract the negatively charged vacancies that diffuse in the lattice if the latter approach it at a nearest neighbour site. It has been calculated using DFT that there is strong binding between the dopant and the vacancy [43]. For the donor atom to diffuse in the lattice it is not enough to just exchange positions with this vacancy, but it has to migrate via the longer-range ring mechanism of diffusion (refer to Figure 2) [81]. This mechanism is effectively dictated by the symmetry of the diamond lattice and, in essence, the vacancy has to migrate in a ring of atoms around the donor atom for the atom to progress to the next lattice position. This ring has to be repeated for every hop of the donor atom in the lattice [43]. There is good agreement between the determined activation energies of diffusion and the ones derived by DFT using the ring mechanism of diffusion for P, As and Sb [42,43]. During the formation of the \(n\)-type regions there is a significant concentration of vacancies that considerably exceeds the concentration of vacancies under equilibrium condition. This interacts with the donor atoms forming D\(V\) pairs, which migrate in the lattice and can lead to larger clusters of the form D\({}_{n}V_{m}\) with n typically up to 4 (refer to Figure 3) [32,35]. These larger clusters are practically immobile; however, they can lead to the deactivation of a significant portion of the donor atoms [35,56]. Codoping strategies were proposed to eliminate or reduce the influence of vacancy defects that control both the diffusion of \(n\)-type dopants and their deactivation [44,45,82,83]. Oversized dopant atoms (such as Sn, Hf and Pb) and carbon reduce the mobility of the donor atoms; however, they do not solve the problem of the formation of defect-dopant clusters that lead to deactivation [54,82]. The most effective defect-engineering strategy was proposed using DFT [83] and was thereafter determined to work using experiments [56,84,85,86,87,88]. Interestingly, this prompted [PERSON] et al. [84] to conclude that F passivation can be used to improve the performance of Ge-based MOSFETs and p-i-n diodes. For Si, it is established that F can be used to suppress self-interstitial and boron (B) diffusion [88,89,90,91,92]. How does fluorine solve the problem of diffusion and deactivation for donor atoms in Ge? The introduction of F atoms in the Ge lattice will result in the saturation of vacancy dangling bonds. This occurs when the migrating F atom encounters a \(V\) in the lattice, and the predicted binding energy of the resultant F\(V\) pair is \(-1.19\) eV [83]. Each vacancy has four dangling bonds, so it can attract up to four F atoms, thus forming F\({}_{4}V\) clusters (binding energy \(-5.00\) eV, schematic representation in Figure 4), whereas every divacancy has six dangling bonds and can form up to the F\({}_{6}V_{2}\) cluster (binding energy \(-8.56\) eV) [83]. The binding energies for the formation of fluorine-vacancy pairs is significantly higher than the binding energies for the formation of donor-vacancy pairs (\(-0.52\) eV for PV to \(-0.70\) eV for Sb\(V\)) [83]. This in turn implies that, if there is a sufficiently high F concentration, the F can attract most of the vacancies in the lattice, thus reducing the  
Figure 2: The ring mechanism of diffusion in a Ge lattice [59]. possibility of the formation of \(\mathrm{D_{n}}V\) (n = 1-4) defects [83]. Consequently, the donor atoms do not have vacancies to diffuse into in the lattice, nor do they have the opportunity to form larger deactivating clusters [83].