^{1}

### Abstract

The self-interaction corrected density-functional calculations are performed for Re impurities and their pairs in silicon.Rhenium ions form in the host crystal not very tight pairs, with impurities separated by one Si atom or by a distance close to two siliconbonds. Comparison of formation energies for various pairs of substitutionals, interstitials, and mixed-site impurities favours the last type. Electron transfer from the interstitial into the substitutional impurity makes the both Re sites nonmagnetic, but the p-type and the n-type co-doping revives magnetism again, the latter more efficiently.

I thank Professor R. R. Gałązka for showing me the experimental results and to Andrzej Fleszar for cross-checking my implementation of the pSIC method to the quantum espresso code with his mixed-basis code. The calculations have been done at the Leibniz Supercomputing Centre in Munich. The work was supported by the European Founds for Regional Development within the SICMAT Project (Contract No. UDA-POIG.01.03.01-14-155/09).

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. SINGLE IMPURITIES AND THE CHARGE TRANSFER BETWEEN THE INTERSTITIAL AND THE SUBSTITUTIONAL RHENIUM IONS

IV. NEUTRAL PAIRS OF RE-IMPURITIES

A. Substitutional pairs

B. Interstitial pairs

C. Mixed substitutional-interstitial pairs

D. Comparison of pairs to singles

V. CHARGED PAIRS OF RE-IMPURITIES

VI. SUMMARY

### Key Topics

- Interstitial defects
- 23.0
- Doping
- 18.0
- Silicon
- 13.0
- Charge transfer
- 10.0
- Rhenium
- 9.0

## Figures

Density of states of (a) the substitutional Re, and (b) the interstitial Re impurities in silicon in the 64-atom neutral supercells, from the pSIC calculations. The Re-5*d* e_{ g } and t_{2} _{ g } states are scaled by two for better visualization. Energy zero is at the Fermi energy.

Density of states of (a) the substitutional Re, and (b) the interstitial Re impurities in silicon in the 64-atom neutral supercells, from the pSIC calculations. The Re-5*d* e_{ g } and t_{2} _{ g } states are scaled by two for better visualization. Energy zero is at the Fermi energy.

Energies of the S-site and the I-site Re in silicon (Δ*E _{f} *), in the neutral and charged 64-atom (65-atom for I) cells, calculated within the pSIC, and given with respect to the energy of the S-site Re. Numbers above the curves denote the charges of the supercells. Numbers in parenthesis denote the total magnetic moments.

Energies of the S-site and the I-site Re in silicon (Δ*E _{f} *), in the neutral and charged 64-atom (65-atom for I) cells, calculated within the pSIC, and given with respect to the energy of the S-site Re. Numbers above the curves denote the charges of the supercells. Numbers in parenthesis denote the total magnetic moments.

Density of states of the S-site and the I-site Re in silicon, calculated with the pSIC method, in (a) the charge negative, (b) the neutral, (c) the charge positive 97-atom cell. Energy zero is at the Fermi energy of given supercell (Fermi energy is not the same for all supercells).

Density of states of the S-site and the I-site Re in silicon, calculated with the pSIC method, in (a) the charge negative, (b) the neutral, (c) the charge positive 97-atom cell. Energy zero is at the Fermi energy of given supercell (Fermi energy is not the same for all supercells).

Formation energies of chosen pairs SS, II, and SI per one Re, with respect to the energies of single impurities S and I. Numbers above the energy levels denote the pair-orientations in the Si crystal.

Formation energies of chosen pairs SS, II, and SI per one Re, with respect to the energies of single impurities S and I. Numbers above the energy levels denote the pair-orientations in the Si crystal.

## Tables

Formation energy (E_{ f }, in eV) for all SS-pairs in the FM state, in the 64-atom cell, with respect to the 220 pair. The magnetization energy (, in meV), and the total magnetization of the cell for the FM state (), as well as the absolute magnetizations for the FM and the AF states () in are also given.

Formation energy (E_{ f }, in eV) for all SS-pairs in the FM state, in the 64-atom cell, with respect to the 220 pair. The magnetization energy (, in meV), and the total magnetization of the cell for the FM state (), as well as the absolute magnetizations for the FM and the AF states () in are also given.

Formation energy (E_{ f }, in eV) for II-pairs in the FM state, in the 66-atom cell, with respect to the 11 pair. The magnetization energy (, in meV), and the total magnetization in the FM state (), as well as the absolute magnetizations for the FM and the AF states () in are also given.

Formation energy (E_{ f }, in eV) for II-pairs in the FM state, in the 66-atom cell, with respect to the 11 pair. The magnetization energy (, in meV), and the total magnetization in the FM state (), as well as the absolute magnetizations for the FM and the AF states () in are also given.

Formation energy (E_{ f }, in eV), with respect to the 333 pair, for all mixed-pairs of the substitutionals and the interstitials in the 65-atom cell.

Formation energy (E_{ f }, in eV), with respect to the 333 pair, for all mixed-pairs of the substitutionals and the interstitials in the 65-atom cell.

Formation energies of the negatively charged SS-pairs with respect to the neutral SS-pairs (E_{ f }, in eV), and the total magnetic moment in the 64-atom cell.

Formation energies of the negatively charged SS-pairs with respect to the neutral SS-pairs (E_{ f }, in eV), and the total magnetic moment in the 64-atom cell.

Formation energies of the positively charged II-pairs with respect to the neutral II-pairs (E_{ f }, in eV), and the total magnetic moment in the 66-atom cell.

Formation energies of the positively charged II-pairs with respect to the neutral II-pairs (E_{ f }, in eV), and the total magnetic moment in the 66-atom cell.

Formation energies of the positively and the negatively charged SI pairs with respect to the neutral SI-pairs (E_{ f }, in eV), and the total magnetic moment in the 65-atom cell.

Formation energies of the positively and the negatively charged SI pairs with respect to the neutral SI-pairs (E_{ f }, in eV), and the total magnetic moment in the 65-atom cell.

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