Unveiling the effects of thallium and bismuth p-n doping on germanium-based clusters (n5 to n12) for applications in semiconductor materials

Abstract

We report a computational investigation utilizing density functional theory (DFT) concerning the pure Gen, as well as their doped analogues (BiGen-1, TlGen-1) and p-n doped BiTlGen-2 clusters with n ranging from 5 to 12. To get a deeper insight in their properties, we focus on the size dependency of these Gen, BiGen-1, TlGen-1, and BiTlGen-2 clusters as well as their shape, relative stabilities, and thermochemical characteristics including binding energy, fragmentation energy, second-order energy difference, and HOMO-LUMO energy gaps. The systematic observations from the data of binding energies indicate that BiGen-1, TlGen-1 and BiTlGen-2 cluster have more structural and thermodynamic stability when compared with the pure Gen clusters. To validate the electronic characteristics of these clusters, additional energy gap-related parameters such as chemical hardness, vertical ionization potentials (VIP), and vertical electron affinities (VEA) are also computed. The doping seems to stabilize the Gen clusters and the highest stability has been achieved for BiGe7, TlGe9, and BiTlGe7 clusters as suggested by the combined effect of all these parameters.