Impact of point defects on the electrical properties of selenium: A density functional theory investigation with discussion of the entropic term

Abstract

Selenium in ambient conditions exhibits two crystalline allotropic forms. The thermodynamically stable phase is the pseudo-1D trigonal form with ${}^{1}{/}_{\ensuremath{\infty}}$[Se] chains. A metastable phase composed of $[{\mathrm{Se}}_{8}]$ rings also coexists. Both are studied herein by means of density functional theory. The recent SCAN functional offers a fair description of both phases. The Birch-Murnaghan equation of states is fitted onto ab initio results to obtain the energy-volume and pressure-energy relationships. Phonon properties (bands and DOS) are computed and a pressure-temperature phase diagram is derived. Intrinsic and extrinsic defect formation enthalpies are also computed using SCAN functional and HSE06-GD3 for the band shifts. The low $p$-type conductivity of the trigonal phase can be attributed to Se self-interstitials while the very low conductivity of the metastable phase is related to very deep native defects. Antimony, and bromine extrinsic defects are tested as potential dopants. Of those three, only antimony in the trigonal phase seems to possibly have a positive impact on the conductivity. Finally, the configurational entropy linked to defect creation is computed. Our calculations clearly show that the usual assumption that defect entropy is negligible compared to the enthalpy seems relevant.