Theoretical and experimental study of positron annihilation with core electrons in solids

Abstract

A theory for calculating the momentum distribution of annihilating positron-electron pairs in solids is presented. To test the theory, momentum distributions are measured by the Doppler broadening of the annihilation radiation for several bulk metals and semiconductors, as well as for semiconductor alloys and for positrons trapped at vacancies in semiconductors. The theory is based on a two-particle description of the annihilating electron-positron pair. Then, the electron-positron correlation effects, i.e., the enhancement of the electron density at the positron, depend on the electronic state in question. The theory is suited for calculating the high-momentum part of the annihilation spectrum that arises from the core electrons and which can be measured by the Doppler broadening using coincidence techniques. The ideas of the theory are justified by a good agreement between theory and experiment in the case of positron annihilation in undefected bulk lattices. Moreover, the comparison of the theoretical and experimental spectra for alloys and vacancy defects tests the theoretical description for the positron distribution in delocalized and localized states, respectively. ͓S0163-1829͑96͒04327-5͔

Modeling the momentum distributions of annihilating electron-positron pairs in solids

“…2 and 3 the Doppler spectra of Cu, Ag, and Al calculated within the both above-mentioned schemes in the logarithmic scale and also normalize the Doppler spectra to the one of Al. The theoretical spectra and ratios are compared with the experimental ones by Nagai et al 35 Both schemes describe the low-momentum region due to the annihilation with valence electrons well but the ratios tell, as seen before, 8 that the state-independent LDA scheme fails to describe the high-momentum region of the Doppler spectra which arises from the annihilation with core electrons. The ratio Cu/ Al ͑see Fig.…”

“…6 The Doppler spectra are calculated using the state-dependent scheme. 8 The momentum distributions are finally convoluted with a Gaussian function with a full width at half maximum ͑FWHM͒ corresponding to the resolution of the Doppler experiment.…”

“…For the description of the many-body effects in the calculation of momentum distributions of annihilating electronpositron pairs we choose finally the so-called state-dependent scheme 8 and for annihilation rates within the state-dependent scheme the local-density approximation ͑LDA͒ enhancement factor parametrized by Boroński and Nieminen. 6 We show that use of the commonly used position-dependent enhancement factor leads to unphysical oscillations at high momenta when one considers ratios of Doppler spectra between two different materials.…”

“…4 In the PAW method the core states are treated in the frozen-core approximation and described using atomic wave functions. 8 In this work, the positron state is solved in the real space using a Rayleigh quotient multigrid ͑RQMG͒ solver. 9 Our scheme gives good results when compared to experiments for delocalized positron states, for which the n + → 0 limit of the TCDFT is exact, as well as for positrons localized at vacancy-type defects.…”

Microscopic identification of native donor Ga-vacancy complexes in Te-doped GaAs

“…The high momentum part of this distribution can be used to identify the chemical surrounding of the annihilation site. [13][14][15][16] This is based on the fact that tightly bound core electrons with high momenta retain their element-specific properties even in a solid. This allows the identification of vacancies and vacancy-impurity complexes, especially when measurements are correlated to calculations of the momentum distribution.…”