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Vacancy in diamond

In an ``ideal'' unrelaxed and neutral vacancy V0, four dangling sp3 hybrids point inwards. The combination of these orbitals in a tetrahedral symmetry gives rise to a nondegenerate state belonging to the a1 representation of the Td symmetry group, and to another triply degenerate state belonging to the t2 representation [56]. The a1 state has the lowest energy and is filled by two of the four electrons of the dangling bonds. The other two electrons occupy the localized t2 state. The energy levels induced by these states fall well inside the band gap. The a1 state ofen appears as a resonance state near the top of the valence band.

Such a partially filled degenerate electronic state t2 is unstable under Jahn-Teller distortion which lowers the symmetry of the structure. The t2 triply degenerate state then splits into a nondegenerate a1 state and a doubly degenerate e state. The two electrons that occupied the t2 state will therefore be in the a1state, and the e state will remain unoccupied, as illustred in figure (5.1).


  
Figure 5.1: Schematic energy-level diagrams for neutral vacancy. The left diagram accounts for an unrelaxed vacancy. The right diagram is after the Jahn-Teller distortion.
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The tetrahedral point group Td has two subgroups, namely D2dand C3v. Each subgroup corresponds to a distortion around the defect, lowering the symmetry to a tetragonal or to a trigonal symmetry, repectively. For each distortion, a specific displacement of the nearest neighbors of the vacancy occurs [71], as shown in figure (5.2). In the case of a neutral vacancy, the tetragonal distortion is dominant. The Jahn-Teller energy is calculated to be few tens of eV, which is relatively low compared to the few eV for the vacancy formation energy.


  
Figure 5.2: Representations of the atomic displacements of the nearest neighbors of a vacancy, induced by a Jahn-Teller effect. The right diagram is a tetrahedral distortion, with a D2d symmetry, and the left one is a trigonal distortion, with a C3v symmetry.
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It has to be mentioned that in the case of the doubly positive vacancy V++ where two electrons are missing with respect to the neutral vacancy, there is no Jahn-Teller distortion since in this case, the t2 state is unoccupied. The distortion exists in the case of the positive vacancy V+, and should be increased with the neutral vacancy since now, there are two electrons in the a1 state. In the negatively charged vacancy V-, the added electron (compared to the neutral vacancy) occupies the higher twofold degenerate e state. A mixed distortion now takes place (tetragonal plus trigonal) to further split the e level into nondegenerate B1 and B2 states, leading to the lower C2v symmetry.

It has to be mentioned that the many-electron effects are negligible with respect to the jahn-Teller effect itself [71]. Therefore, the one-elecron picture of the tight binding model may be suitable to reproduce the energy levels associated with the vacancy defect. Song et. al. [72] studied intrinsic point defects in crystalline silicon by tight binding molecular dynamics. In particular, the lattice distortion induced by Jahn-Teller effect is well reproduced, and corresponding energy levels are obtained in the band gap.

In experiment, a so called GR1 band is measured, associated with an optical transition at the neutral vacancy V0 between the levels mentioned above. This signal is observed in an irradiated or implanted sample, which suggests that vacancies are created during this process and remain relativly stable, untill annealing at high enough temperature is carried out.


next up previous contents
Next: The <100> split-interstitial Up: Electronic structure of defects Previous: Electronic structure of defects
David Saada
2000-06-22