Ab-Initio Studies of Acceptor Impurities and Stability of Complexes in Ge

Abstract

The application of germanium (Ge) as a promising material for complementary metal-oxide semiconductors (CMOS) technology is attracting attention due to its narrow band gap, high carrier mobility and low voltage operations. Recent experimental and theoretical studies revealed that dopants in Ge cluster with vacancies forms with lower energies and contribute to low activation of dopants impurity in Ge. DFT electronic simulation have been used to provide concise information about the formation of defect clusters and complexes that influence diffusion mechanisms in Ge. Our main objective in this study is to use simulations based on ͑DFT to calculate the structural, electronic properties and interactions between acceptors and Ge in different configurations with a view to finding the most energetically stable configuration of various defect complexes in Ge. By means of density functional theory (DFT), we present ab-initio calculation of interactions between A (A: Be,Mg, Ca, Sr, Ba, Ga, In) vacancy complexes (A-VGe) and vacancy-interstitial complexes (A-VGeIA) in two configurations of the hexagonal (H) and tetrahedral (T) in Ge. These calculations employed a projector augmented wave (PAW) pseudopotentials within the generalized gradient approximation (GGA). The geometric structures and formation energies of A-VGe and A-VGeIA in both the T and H configurations for the neutral charge state were obtained. The formation energies of A-VGe were low and energectically favourable with Ga-VGe and Ca-VGe forming with the lowest formation energies at -1.24 and -0.38 eV respectively. For the A-VGeIA, the results of the H configuration were more energetically favourable and forms with lower formation energies than the T configuration. The Ca-VGeICa and Be-VGeIBe forms with the lowest formation energies of -2.59 and -1.49 eV respectively. The stability of the A-VGeIA and A-VGe complexes in Ge were obtained from their binding energies. The binding energies (Eb ) which are defined as the energy required to split up the defects cluster into well separated non-interacting defect is given as Eb = E(formation)(VGe) + E(formation)(AGe) - E(formation){defect-complex}, where E(formation)(VGe), E(formation)(AGe) and E(formation)(defect-complex) are the formation energies of the neutral charge state of the germanium vacancy, interstitials and defect-complexes. The above equation could be interpreted as the energy gain of the bonded structure with respect to the isolated components. Positive binding energies suggest that the defect complexes are stable and cannot easily dissociate. The calculated binding energies of both the A-VGe and the A-VGeIA displayed the ability of these complexes to form without dissociation. For the A-VGeIA, the H configuration forms with more favourable binding energies than the T configuration. In summary the detailed calculated results we have presented are expect to be useful in the process modeling of Ge-based devices.