Energy levels of isolated interstitial hydrogen in silicon

Abstract

This paper first describes the quantitative determination of the static and dynamic properties of the locally stable states of monatomic hydrogen dissolved in crystalline silicon: ${\mathrm{H}}^{+},$ ${\mathrm{H}}^{0},$ and ${\mathrm{H}}^{\mathrm{\ensuremath{-}}}.$ The monatomic hydrogens were created controllably near room temperature by using hole-stimulated dissociation of phosphorus-hydrogen (PH) complexes. Drift velocities and charge-change rates were studied via time-resolved capacitance-transient measurements in Schottky diodes under changes of bias. These data enable the donor level ${\ensuremath{\varepsilon}}_{D}$ of ${}^{2}\mathrm{H}$ to be located at \ensuremath{\sim}0.16 eV below the conduction band (confirming that the ${E3}^{\ensuremath{'}}$ center found in proton-implanted Si corresponds to interstitial H in undamaged Si), and the acceptor level ${\ensuremath{\varepsilon}}_{A}$ at \ensuremath{\sim}0.07 eV below midgap, so that hydrogen is a ``negative-U'' system. The experimental values of ${\ensuremath{\varepsilon}}_{D}$ and ${\ensuremath{\varepsilon}}_{A}$ are consistent with predictions from first-principles calculations, which also provide detailed potential-energy surfaces for hydrogen in each charge state. While the phonon-mediated reaction ${\mathrm{H}}^{0}\ensuremath{\rightarrow}{\mathrm{H}}^{+}{+e}^{\ensuremath{-}}$ is fast, the reaction ${\mathrm{H}}^{\ensuremath{-}}\ensuremath{\rightarrow}{\mathrm{H}}^{0}{+e}^{\ensuremath{-}}$ has an activation energy \ensuremath{\sim}0.84 eV, well above the energy difference (\ensuremath{\sim}0.47 eV) between initial and final states. Our experiments also yielded diffusion coefficients near room temperature for ${}^{1}{\mathrm{H}}^{+},$ ${}^{2}{\mathrm{H}}^{+},$ and ${}^{2}{\mathrm{H}}^{\mathrm{\ensuremath{-}}}.$ The asymmetrical positioning of ${\ensuremath{\varepsilon}}_{D}$ and ${\ensuremath{\varepsilon}}_{A}$ in the gap accounts for many previously unexplained effects. For example, it is shown to be responsible for the much greater difficulty of passivating phosphorus-doped than comparably boron-doped Si. And while modest hole concentrations dissociate PH complexes rapidly at temperatures where thermal dissociation takes years, we could not detect an analogous dissociation of BH complexes by minority electrons, a process that is expected to be frustrated by the rapid thermal ionization of ${\mathrm{H}}^{0}.$ The distribution of hydrogen in n-on-n epitaxial layers hydrogenated at 300 \ifmmode^\circ\else\textdegree\fi{}C can be accounted for if the donor-hydrogen complexes are in thermal equilibrium with ${\mathrm{H}}_{2}$ complexes whose binding energy (relative to ${\mathrm{H}}^{+}{+\mathrm{H}}^{\mathrm{\ensuremath{-}}})$ is of the order of 1.75 eV. With this binding energy, the measured migration of ${\mathrm{H}}_{2}$ at 200 \ifmmode^\circ\else\textdegree\fi{}C and below must be by diffusion without dissociation.