Multiple trapping of hydrogen at boron and phosphorus in silicon

We present theoretical studies on the trapping of two hydrogen interstitials at boron and phosphorus dopants in crystalline silicon. A large number of a priori possible configurations arising from the interactions of the dopant and two hydrogens are investigated at the approximate ab initio Hartree-Fock level with various basis sets and molecular clusters containing up to 48 host atoms. We computed and compared equilibrum geometries, electronic structures, and relative stabilities of the complexes. Our results show that the {B,H,H} and {P,H,H} defects are energetically preferred over other known or expected forms of hydrogen (dimer, single interstitial) in hydrogen-passivated material, in which dangling-bond defects (vacancies, grain boundaries, etc.) are absent. The most stable configurations {B,H,H} (in p-type Si) and {P,H,H} (in n-type Si) almost certainly traps for additional hydrogens. The results of our calculations strongly argue in favor of multiple trapping of H at shallow dopants, if the concentration of H interstitials is sufficiently high as is realized, e.g., within the first micrometer in plasma-exposed Si surfaces.