Energetics of positron states trapped at vacancies in solids

We report a computational first-principles study of positron trapping at vacancy defects in metals and semiconductors. The main emphasis is on the energetics of the trapping process including the interplay between the positron state and the defect’s ionic structure and on the ensuing annihilation characteristics of the trapped state. For vacancies in covalent semiconductors the ion relaxation is a crucial part of the positron trapping process enabling the localization of the positron state. However, positron trapping does not strongly affect the characteristic features of the electronic structure, e.g., the ionization levels change only moderately. Also, in the case of metal vacancies, the positron-induced ion relaxation has a noticeable effect on the calculated positron lifetime and momentum distribution of annihilating electron-positron pairs.

Figure 1

Configuration-coordinate diagrams for (a) the monovacancy in Al and (b) the neutral monovacancy in Si. The dotted lines show the positron energy eigenvalue (relative to the one in perfect bulk), the dashed lines correspond to the energy of the lattice and the delocalized positron, and the solid lines are the total energy of the defect-positron system as functions of the relaxation of the vacancy. The positive (negative) sign denotes outward (inward) relaxation. Points A, B, and C denote different stages in the positron trapping process.

Figure 2

Positron densities in monovacancies (left, contour spacing of $0.01{\mathrm{\AA }}^{-3}$) in Al, Fe, and Si and corresponding perfect lattices (right, contour spacing one-tenth of the maximum value). The dots in the figures denote the locations of the nuclei on the plane.

Figure 3

(Color online) The density of the localized electron state at a neutral Si vacancy when (a) there is no localized positron at the vacancy ($D_{2d}$ symmetry) and (b) a positron is localized at the vacancy (symmetric $T_d$).

Figure 4

Total energy (zero level arbitrary) of a system comprised of a positron and the Ga vacancy in GaAs as a function of the charge state of the vacancy and electron chemical potential ${\mu }_e$. The positron is either trapped at the vacancy or in the delocalized bulk state.

Figure 5

The experimental and calculated Doppler spectra (ratio to bulk) of triply negative Ga vacancies in GaN (엯, dash line) and GaAs (●, solid line). The experimental data are from Refs. 40, 41, respectively.