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 $(n\gtrsim {10}^{18}{\mathrm{cm}}^{-3})$, the positronium fraction ($I_{\mathrm{Ps}}$) increased above 700 K and reached more than 95% at 1000 K. In undoped and lightly doped Si ($n$, $p\lesssim {10}^{15}{\mathrm{cm}}^{-3}$), $I_{\mathrm{Ps}}$ decreased from 300 to 500 K and increased above 700 K. In heavily doped $p$-type Si ($p\gtrsim {10}^{18}{\mathrm{cm}}^{-3}$), $I_{\mathrm{Ps}}$ 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.

Figure 1

Annihilation $\gamma$-ray spectra at 511 keV obtained for Ge(111) at 1000 and 300 K with positron energies of $E_{+}=200$ eV and $E_{+}=30$ keV, respectively. In the latter condition, positronium formation is negligible.

Figure 2

Temperature dependences of positronium fraction obtained for the Si(111) and Si(001) samples with different doping conditions. Filled and open circles are obtained in the cooling and heating runs, respectively. Solid lines are the fitting curves using Eqs. (5, 6, 7).

Figure 3

Positronium fraction obtained for the doped and undoped Si(111) samples at 373 K ($100{}^{\circ }\mathrm{C}$) as a function of incident positron energy.

Figure 4

Positronium time-of-flight (Ps-TOF) spectra obtained for the Si(111) samples for different doping conditions at the highest (1000 K), medium (573 and 673 K) and lower (373 and 348 K) temperatures. Vertical broken lines denote the threshold of the TOF spectra ($\sim 1.5$ eV). Arrows denote the approximate peak positions of two types of Ps distinguished by their energies.

Figure 5

Schematic representations of (a) temperature dependence of positronium fraction for the three typical doping conditions shown in Fig. 1, and (b) temperature ranges of type A and type B positronium distinguished by their energies.

Figure 6

Schematic representations of (a) band bending effect on positrons, (b) electron-hole plasma created by positron impact and resultant positronium formation, (c) positronium formation via work function mechanism, and (d) positronium formation via surface positron state.