New Mechanism for Positronium Formation on a Silicon Surface

We describe experiments in which positronium (Ps) is emitted from the surface of $p$-doped Si(100), following positron implantation. The observed emission rate is proportional to a Boltzmann factor $\exp \{-E_A/kT\}$, which is dependent on the temperature $T$ of the sample and a characteristic energy $E_A=(0.253\pm 0.004)\mathrm{eV}$. Surprisingly, however, the Ps emission energy has a constant value of $\sim 0.16\mathrm{eV}$, much greater than $kT$. This observation suggests the spontaneous emission of energetic Ps from a short-lived metastable state that becomes thermally accessible to available surface electrons once the positron is present. A likely candidate for this entity is an electron-positron state analogous to the surface exciton observed on $p$-Si(100) $c(4\times 2)$ by Weinelt et al. [Phys. Rev. Lett. 92, 126801 (2004)].

Figure 1

Ps yield as a function of temperature using a low density (unbunched) positron beam (a) and with a higher density bunched beam with and without a resonant $1S\mathrm{\text{−}}2P$ laser (b). A decomposition of the total yield into various components is shown in (c), with the total Ps curve being proportional to the laser-off fit of (b). The solid line in (a) is a fit to the data using Eq. (1). The inset in (b) shows a time of flight spectrum taken at 650 K. Errors bars are smaller than the symbols.

Figure 2

$1S\mathrm{\text{−}}2P$ line shapes measured for different sample temperatures at $\theta =0°$ (a) and $\theta =68°$ (b). The curve in (a) is a spline fit to the average of the high temperature measurements (open symbols). The same curve is superimposed on top of the lower temperature measurements (filled symbols) to emphasize the presence of a low amplitude component having a full width at half maximum (FWHM) that is about twice that of the main component. In (b) the curve is a two-Gaussian fit to the high temperature data. The Ps energies derived from (a) and (b) are shown in (c), and the solid line in this figure is $kT/2$.

Figure 3

Schematic of electron and positron energy levels. The observed processes A, B, and C described in the text are indicated, along with another (unobserved) possibility D, which is the thermal desorption of Ps with electrons from the $D_{\mathrm{up}}$ band. Here $e\mathrm{\text{−}}h$ refers to electron-hole pairs created by the incident positron beam that directly populate the PsX state. The electron and positron energy scales have opposite senses so that the kinetic energy of Ps formed from a given pair of electron and positron levels is equal to the vertical separation of the two levels. The 0 eV electron reference level is the VBM. The 0 eV positron reference level is that of a free positron in vacuum with zero kinetic energy. The electron vacuum level is 5.4 eV above the VBM and coincides with the $-6.8\mathrm{eV}$ positron level corresponding to vacuum Ps at rest.