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| Paper IPM / P / 7664 |
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| Abstract: | |||||||||||||||
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Symmetric lattice relaxation around a vacancy in diamond and its
effect on many electron states of the defect have been
investigated. A molecular approach is used to evaluate accurately
electron-electron e−e interaction via a semiempirical formalism
which is based on a generalized Hubbard Hamiltonian. Coupling of
the defect molecule to surrounding bulk is also considered using
an improved Stillinger-weber(SW)potential for diamond. Strong
dependence of the electronic energy levels to the relaxation size
of the nearest neighbor NN atoms indicates that in order to obtain
quantitative results the effect of lattice relaxation should be
considered. Except for the high spin state of the defect
5A2, the order of other lowest levels, particularly the
ground state of the vacancy 1E does not change by the
relaxation. At 12 % outward relaxation, there is a level
crossing between 5A2 and the excited state of the well
known GR1 transition 1T2. The reported level crossing
confirms the predicted relative energies of these states in the
band gap that was speculated by monitoring the temperature
dependence of the electron paramagnetic resonance (EPR) signal. By
considering the outward relaxation effect, we obtained midgap
position for the 5A2 state in agreement with the
suggestion made by EPR. The position of the low lying 3T1
level varies from 100 to 400 meV with increasing outward
relaxation. When the ion-ion interaction of the NN atoms is
included the outward relaxation lowers the energies of all
electronic states. The relaxing force is different for
investigated electronic states. By considering the interaction of
the first and second shell neighbors of the vacancy the calculated
elastic barrier restricts outward relaxation of the vacancy to 12% for the ground and 18% for the 5A2 excited state.
The calculated equilibrium bond lengthes are in very good
agreement with ab initio density functional theory (DFT) and EPR
measurement data. Electronic configurations in the unrelaxed and
relaxed eigenfunctions of the Hamiltonian are reported. Our
results also suggest that there is an outward relaxation if Hund
rule is applicable.
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