Charge state and hydration of vacancies in silicon and silicon carbide in contact with water: A grand-canonical first-principles stability map

Abstract

The state of a vacancy in a semiconductor is normally described by the Fermi level alone. In wet-etched, electrochemically processed, or humid silicon and silicon carbide, a vacancy also takes up hydrogen and oxygen from water, in amounts set by pH and electrode potential. We treat both effects together by minimizing the grand potential of a vacancy complex over its charge state and hydrogen/oxygen content. The result is a stability map in Fermi level and hydrogen chemical potential, which the computational hydrogen electrode relates to pH and potential. We parameterize it with spin-polarized density functional theory in 64-atom cells, including the vibrational free energy of bound H and O, for the silicon vacancy, its H, O, and OH complexes, and both vacancies of 3C-SiC. Hydrogen binds cooperatively to the silicon vacancy, which goes directly from bare to fully passivated $V$H$_4$. In contact with water the bare vacancy is never the lowest-energy state. Near neutral pH it binds oxygen from water as the A center, the paramagnetic hydroxyl complex forms below about pH 5 at zero bias, and full passivation to $V$H$_4$ requires cathodic bias. In PBE the Fermi level barely moves these boundaries, because the acceptor levels lie at or above the conduction-band edge. In SiC the first hydrogen binds to the silicon vacancy by 1.97 eV but is unbound at the carbon vacancy (the $Z_{1/2}$ center), so hydrogen from water alone should not passivate it except under cathodic bias.