There is a strong interest to use germanium as an active device layer in deep sub-micron devices. This imposes similar stringent material and process requirements for germanium as for silicon. Lattice defect formation during crystal growth and device processing as well as dopant diffusion and activation are to a large extent controlled by the intrinsic point defects in the semiconductor. The properties of the vacancy and the self-interstitial in germanium are, however, not well known. The scarce available experimental data are combined with ab initio and molecular-dynamics calculations and other published simulation results. Based on this a best estimate is made for the formation and migration energies of the vacancy and the self-interstitial in germanium.
Density functional theory with local density approximation including on-site Coulomb interaction has been used to calculate the formation energy of the neutral and charged vacancy in germanium as a function of the Fermi level. The calculations suggest that vacancies in germanium are multiple-level acceptors with a first level at 0.02eV and a second level at 0.26eV above the valence band maximum in agreement with published experimental data. The formation energies of the neutral and charged vacancies line up well with the experimental values estimated from quenching experiments.
During the last decade, considerable progress has been made in understanding the properties and behavior of the vacancy V and self-interstitial I in silicon (Si) and germanium (Ge) crystals. This is to a large extent due to the maturing of density functional theory (DFT) calculation techniques and the increase of computing power enabling to calculate not only the formation and migration energies of V and I, but also the interaction with impurities and with crystal surfaces. Furthermore, the impact of internal and external stress on formation and migration enthalpies of both intrinsic point defects has been clarified recently. In this paper an overview is given on recent assessments on the properties of intrinsic point defects in Si and Ge, and on the useful application of DFT calculations for the control and engineering of intrinsic point defects in Si and Ge single crystal growth from a melt.
Electronic and magnetic properties of Mn ∕ Ge digital ferromagnetic heterostructures: An ab initio investigation J. Appl. Phys. 99, 08D705 (2006); 10.1063/1.2172542 Energy band gaps and lattice parameters evaluated with the Heyd-Scuseria-Ernzerhof screened hybrid functional Efficient hybrid density functional calculations in solids: Assessment of the Heyd-Scuseria-Ernzerhof screened Coulomb hybrid functionalThe revised Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE06) is used for calculating the formation and migration energies of the vacancy in Ge, and the results are compared with those previously obtained using the local density approximation with the on-site Coulomb interaction U (LDAþU) approach and with other published results. It is demonstrated that using HSE06 gives a much more accurate electronic description of the vacancy and yields an excellent estimate of the activation energy of self-diffusion in Ge consistent with experimental data. The migration energies of the vacancy in different charge states calculated with the HSE06 approach agree well with the results of low-temperature infrared-absorption measurements. In contrast to previous results, the HSE06 calculations suggest that vacancies in Ge are multiple-level acceptors with levels located in the upper half of the bandgap. This can explain the observed high density of acceptor-like interface traps near the conduction band, pinning the Fermi level and inhibiting the formation of an inversion layer in n-channel devices in Ge.
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