Angle-resolved energy distribution of re-emitted positrons from a W(100) single crystal

Angular distribution of backward re-emitted positrons from a W(100) single crystal have been measured for incident positron energies of 250 and 600 eV. The width of the angular distribution was broader than that predicted by a model of re-emission that assumes complete thermalization of positrons in the solid. Angle-resolved energy distribution of re-emitted positrons showed that the mean energy of the emitted positrons increased with angular deviation from normal. The increase is explained in terms of energy-dependent refraction of positrons traversing the potential step at the surface. The results are in qualitative agreement with a one-dimensional step model of positron re-emission. The observed angular distribution and energy distributions qualitatively matched calculated data if a sample effective temperature of four times the actual temperature is assumed. This suggests the emission of incompletely thermalized positrons at low energy of incident positrons.

Figure 1

A schematic of the experimental arrangement for measuring re-emitted positron energy and angular distributions. The orientation of the sample ($O^{\prime }$) with $N^{\prime }$ as its surface normal shown with dotted lines is obtained by rotating the sample by θ from the initial orientation ($O$ with $N$ as normal).

Figure 2

Positron counts with retarding bias on grid (filled circles) and negative of its derivative showing the energy spectrum (open circles) at incident positron energy of 600 eV.

Figure 3

(a) Angular distribution of backward re-emitted positrons from W(100) at an incident energy of 250 (circle) and 600 eV (square) and forward re-emitted positrons from 1000-Å W(100) film with 5 keV incidence energy from Chen et al. (Ref. 13). The open symbols correspond to transposed data with respect to normal to the crystal surface. Caclulated data is with $T_{\mathrm{eff}}$ $=$ 4$T_{\mathrm{samp}}$ [see legend of (b) for details]. (b) Calculated angular distributions with various parameters (effective temperature and acceptance angle) in terms of 1D step model of positron re-emission. The ${\varphi }^{+}$ $=$ −2.93 eV and ($m^{*}/m$) $=$ 1. Gaussian fit to the experimental angular distribution is also shown in the figure as filled circles.

Figure 4

(a) Retarding curves of positron emitted at various angles with respect to the normal to the surface. Total numbers of positrons are normalized. (b) The energy distribution of positrons emitted at different angles. The lines are Gaussian fit to the data.

Figure 5

Change in mean energy of the re-emitted positrons with emission angle with respect to the normal to the surface.

Figure 6

Experimental and calculated energy spectra of re-emitted positrons at various angles. The calculated data are ten-point smoothened by adjacent averaging to match the experimental procedures adopted in measuring the energy spectra.