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

Abstract

Measuring the Doppler broadening of the positron annihilation radiation or the angular correlation between the two annihilation gamma quanta reflects the momentum distribution of electrons seen by positrons in the material. Vacancy-type defects in solids localize positrons and the measured spectra are sensitive to the detailed chemical and geometric environments of the defects. However, the measured information is indirect and when using it in defect identification comparisons with theoretically predicted spectra is indispensable. In this article we present a computational scheme for calculating momentum distributions of electron-positron pairs annihilating in solids. Valence electron states and their interaction with ion cores are described using the all-electron projector augmented-wave method, and atomic orbitals are used to describe the core states. We apply our numerical scheme to selected systems and compare three different enhancement ͑electron-positron correlation͒ schemes previously used in the calculation of momentum distributions of annihilating electron-positron pairs within the density-functional theory. We show that the use of a state-dependent enhancement scheme leads to better results than a position-dependent enhancement factor in the case of ratios of Doppler spectra between different systems. Further, we demonstrate the applicability of our scheme for studying vacancy-type defects in metals and semiconductors. Especially we study the effect of forces due to a positron localized at a vacancytype defect on the ionic relaxations.

Energetics of positron states trapped at vacancies in solids

“…Besides the agreement with the 2CDFT, the results obtained with the conventional scheme also compare reasonably well with experiment. 18,23 First and foremost, the measured changes in the positron lifetime and in the relative changes in the core annihilation rate between the vacancy and bulk states are reproduced.…”

“…Our computational methods are described in more detail in Ref. 18 and, here, we will give only the main features. We perform electronic-structure calculations within the LDA.…”

“…For delocalized positron states in perfect bulk solids, there exist several systematic comparisons, [15][16][17][18] but for positron states trapped at vacancy defects, comparisons treating several materials and systems on the same footing are scarce. The reason may be in difficulties arising in the theoretical description, e.g., in the density-functional theory 19,20 ͑DFT͒, the local-density approximation ͑LDA͒ for the electron exchange and correlation underestimates the energy band gap in semiconductors which may have severe consequences on the localized electron states and the ionic structure at defects.…”

Identifying vacancy complexes in compound semiconductors with positron annihilation spectroscopy: A case study of InN

“…Adding negative (positive) charge is expected to lead to an additional inward 125201-2 (outward) relaxation, 11 while the Coulomb force of localized positrons is directed outward. 25 The exact charge state of defect complexes is often unknown in experiments, hence it is not safe to be assumed without further proof. On the other hand, only considering the positron-induced forces 31 leads to an overestimation of the outward relaxation.…”

“…Recent attempts, however, have shown that these limitations could in principle be overcome by careful modeling of positron annihilation parameters using ab initio calculations. [23][24][25] Despite this, to the best of our knowledge, a comprehensive theoretical study of positron annihilation in InN is still missing.…”