We theoretically investigate the impurity doping effects on the structural parameters such as lattice constant, atomic positions, and site preferences of impurity dopants for Al-doped magnesium silicide (Mg 2 Si) crystal using the first-principles calculation methods. We present comparison between several codes: ABCAP, Quantum Espresso, and Machikaneyama2002 (Akai KKR), which are based on the full-potential linearized augmented plane-wave method, the pseudopotential method, and KKR/GGA Green's function method, respectively. As a result, any codes used in the present study exhibit qualitative consistency both in the dependence of the lattice constants on the doping concentration and the energetic preference of the Al atom for the following sites; substitutional Si and Mg sites, and interstitial 4b site; in particular, ABCAP, which is based on the all-electron full-potential method, and Quantum Espresso, which is a code of the pseudopotential method, produce closely-resemble calculation results. We also discuss the effects of local atomic displacement owing to the presence of impurities to the structural parameters of a bulk. Using the analytical method considering the local atomic displacement, moreover, we evaluate the formation energy of Na-and B-doped systems as examples of p-type doping in order to examine the possilbility of realizing p-type Mg 2 Si.
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