Density functional theory study of dopant effect on formation energy of intrinsic point defects in germanium crystals

During the last decade the use of single crystal germanium (Ge) layers and structures in combination with silicon (Si) substrates has led to a revival of defect research on Ge. Ge is used because of the much higher carrier mobility compared to Si, allowing to design devices operating at much higher frequencies. A major issue for the use of Ge single crystal wafers is the fact that all Czochralski-grown Ge (CZ-Ge) crystals are vacancy-rich and contain vacancy clusters that are much larger than the ones in Si. In contrast to Si, control of intrinsic point defect concentrations has not yet been realized at the same level in Ge crystals due to the lack of experimental data especially on dopant effects. In this study, we have evaluated with density functional theory (DFT) calculations the dopant effect on the formation energy (Ef) of the uncharged vacancy (V) and self-interstitial (I) in Ge and compared the results with those for Si. The dependence of the total thermal equilibrium concentrations of point defects (sum of free V or I and V or I paired with dopant atoms) at melting temperature on the type and concentration of various dopants is obtained. It was found that (1) Ge crystals will be more V-rich by Tl, In, Sb, Sn, As and P doping, (2) Ge crystals will be more I-rich by Ga, C and B doping, (3) Si doping has negligible impact. The dopant impact on Ef of V and I in Ge has a narrower range and is smaller than that in Si. The obtained results are useful to control grown-in V and I concentrations, and will perhaps also allow to develop defect-free “perfect” Ge crystals.