Atomistic study of intrinsic defects in Germanium

Since high-k insulators appear more and more to be preferable to SiO2 in semiconductor technology, Ge is again becoming of increasing interest, since its carrier mobility is higher than that of Si. Atomistic simulations are a powerful tool to investigate atomic-level physics and to get a better understanding of the processes during the technological steps in integrated electronic device manufacturing.
In the present work different interatomic potentials for Ge are evaluated with respect to their accuracy in describing the structure and energetics as well as the migration of point defects. A number of parameterizations of the Stillinger-Weber (SW) potential and one Tersoff type potential were tested.
The formation energies for different configurations of the interstitial are calculated. Also the formation energy of the vacancy and the bond defect are estimated. It can be shown that the extended 110-dumbbell configuration is the interstitial with the lowest formation energy for most SW parameter sets. In the Tersoff case the tetrahedral interstitial shows the lowest formation energy. For the SW-type potentials the vacancy shows a strong inward-distortion, whereas for the Tersoff potential it shows a slight outwards-distortion.
In recent ab-initio calculations the 110 dumbbell has been found to be the most stable interstitial structure. This is in qualitative agreement with the results for most SW parameter sets, although these calculations predict the extended dumbbell configuration as the interstitial with the lowest formation energy. For the SW parameter sets of W. Yu (model B) and Nordlund, the formation energy of this dumbbell is also in qualitative agreement with the ab-initio result. The formation energy of the vacancy obtained with these SW parameter sets is nearly equal to the ab-initio result. The observed inwards relaxation of the atoms around the vacancy is also found by ab-initio calculations. However, the details of the lattice distortion near the vacancy and the interstitial differ from those predicted by ab-initio calculations.
For the reasons mentioned above, the SW parameter sets of Nordlund et al. and W. Yu et al. are selected for migration investigations. In both cases the vacancy mobility strongly dominates interstitial mobility. Some investigations are also performed with the Tersoff potential, where the vacancy shows a very low mobility.
The results are used to estimate the self-diffusion coefficient. With the SW approach it is shown that self-diffusion in Ge is mediated by vacancies. This stands in good agreement with experimental data. However, the calculated migration energy (2.2 eV) is less than the measured value (3.09 eV). With the Tersoff potential an interstitial dominated mechanism is found. Therefore the Tersoff potential cannot be considered useful for a study of point defect and self-diffusion in Ge.