Positronium formation at Si surfaces

Positronium formation at Si(111) and Si(001) surfaces has been investigated by changing the doping level systematically over the range 300--1000 K. The temperature dependence of the positronium fraction varied with the doping condition, and there were practically no differences between the two surface orientations. In heavily doped $n$-type Si $(n\ensuremath{\gtrsim}{10}¹⁸\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3})$, the positronium fraction (${I}_{\mathrm{Ps}}$) increased above 700 K and reached more than 95% at 1000 K. In undoped and lightly doped Si ($n$, $p\ensuremath{\lesssim}{10}¹⁵\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$), ${I}_{\mathrm{Ps}}$ decreased from 300 to 500 K and increased above 700 K. In heavily doped $p$-type Si ($p\ensuremath{\gtrsim}{10}¹⁸\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}3}$), ${I}_{\mathrm{Ps}}$ increased in two steps: one at 500--600 K and one above 700 K. Overall, the positronium fraction increased with the amount of $n$-type doping. These phenomena were found to be dominated by two kinds of positronium with energies of 0.6--1.5 eV and 0.1--0.2 eV, which were attributed to the work-function mechanism and the surface-positron-mediated process, respectively, with contributions from conduction electrons. The positron work function was estimated to be positive. This agrees with first-principles calculation. The positive positron work function implies that the formation of excitonic electron-positron bound states begins in the bulk subsurface region and transits to the final positronium state in the vacuum.