Annealing dynamics of irradiation-induced defects in high-purity silicon in the presence of hydrogen

Abstract

A reaction model explaining (i) the hydrogen-mediated transformation of the vacancy-oxygen ($V$O) center into a vacancy--oxygen-hydrogen center ($V$OH${}^{*}$), with an energy level at $0.37\phantom{\rule{0.16em}{0ex}}\mathrm{e}\mathrm{V}$ below the conduction-band edge (${E}_{\mathrm{c}}$), and (ii) the passivation of the divacancy center is presented. $V$OH${}^{*}$ dissociates with a rate of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$ at $195{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\phantom{\rule{0.16em}{0ex}}\mathrm{C}$, causing $V$O to recover after long duration ($>$${10}^{4}\phantom{\rule{0.16em}{0ex}}\mathrm{min}$), while a similar evolution occurs at ${300}^{\ensuremath{\circ}}\mathrm{C}$ on a time scale of the order of $10\phantom{\rule{0.16em}{0ex}}\mathrm{min}$. The diffusivity of the monatomic hydrogen used in the model agrees closely with the established values for the diffusivity of protons. After the recovery of $V$O, further annealing at higher temperatures and/or longer durations transforms $V$O into the ``ordinary'' vacancy--oxygen-hydrogen center with an energy level at ${E}_{\mathrm{c}}\ensuremath{-}0.32\phantom{\rule{0.16em}{0ex}}\mathrm{e}\mathrm{V}$ ($V$OH). $V$OH is subsequently transformed into $V$OH${}_{2}$. For temperatures above $250{\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}\mathrm{C},$ two additional hydrogen-related levels occur ($\ensuremath{\sim}0.17$ and $\ensuremath{\sim}$$0.58\phantom{\rule{0.16em}{0ex}}\mathrm{e}\mathrm{V}$ below ${E}_{\mathrm{c}}$) with a one-to-one ratio and a possible association with different charge states of a ${V}_{2}$OH center is discussed.