Formation Energy of Intrinsic Point Defects in Si and Ge and Implications for Ge Crystal Growth

Abstract

The formation energies of intrinsic point defects in Si and Ge were calculated by means of Density Functional Theory applying thin film models. The obtained formation energy for a Ge vacancy is close to the value calculated by means of a hybrid exchange correlation potential (HSE06). Well accepted experimental data exist for the sum of the formation and migration energies of vacancies and self-interstitials in Si. Taking into account recent values for the migration energies of point defects, the results of the present study are in excellent agreement with the experimental data. Applying the thin film model for both Si and Ge, one can compare formation energies of intrinsic point defects for both semiconductors. The thermal equilibrium concentration of Ge self-interstitials is more than one order of magnitude lower than that of Si interstitials while the vacancy concentrations are of similar magnitude. Contrary to Si, the diffusivity of Ge self-interstitials cannot recover the unbalance of the thermal equilibrium concentrations even if the growth rate is reduced to very low values. Therefore, Ge crystals grown from a melt are always vacancy-rich which results in void formation independent of the growth condition.