Charge State Dependent Jahn-Teller Distortions of the $E$-Center Defect in Crystalline Si

The atomic and electronic structures of a lattice vacancy trapped next to an As impurity (the $E$-center defect) in crystalline Si are investigated using ab initio pseudopotential total energy calculations. Jahn-Teller distortions and energies, reorientation barriers, defect wave function characters, and hyperfine coupling parameters associated with ($-$) and (0) charge states of the $E$ center are calculated using a combination of real-space cluster and plane wave supercell methods. For the first time in the theoretical study of this defect, the senses of the Jahn-Teller distortions in the two charge states are found to be opposite, changing from a large pairing type in $(0)$ to a large resonant-bond type distortion in the $(-)$ charge state, in agreement with experimental data.

Figure 1

Atomic structure of the ideal As-$V$ pair (top), and electronic structure, level symmetries, and corresponding atomic structures viewed along the [111] As-$V$ pair axis for large pairing distortions of the $(0)$ charge state (bottom left) and large resonant bond distortions of the $(-)$ charge state (bottom right).

Figure 2

Relaxed minimum-energy atomic structures in the first shell around the $E$ center in its neutral (left) and negatively charged (right) states. Arsenic atom is represented by the gray circle. All distances between Si atoms are in Å. The second nearest neighbor distance in bulk Si is $3.84\AA$. Both figures have a reflection symmetry with respect to the plane passing through the As-$V$ axis and the apex Si atom.

Figure 3

Charge density contour plots for the highest occupied levels $a^{\prime }$ (left) and $a^{\prime \prime }$ (right) for the $(0)$ and $(-)$ charge states of the $E$ center, respectively. The contour planes in both cases pass through the three Si atoms (filled circles) near the vacant site. Both figures are nearly to scale with respect to calculated interatomic distances.

Figure 4

Reorientation barrier calculations (left) for the As-$V$ axis via vacancy migration through the sixfold ring of the Si lattice (right). The points (◇, □, ×) correspond to actual calculations for three cluster sizes fitted to smooth curves. The smallest cluster does not allow full relaxations along the $(1)\to (2)$ path, due to not allowing H-passivated Si atoms to move. The solid, gray, and open circles correspond to Si, As atoms, and the vacant site, respectively.