10. Appendix

A4.1 A Prototypical Deep Center in N-Type Zincblende-Type Semiconductors 681
a negative on-site Coulomb interaction U (abbreviated as -U) between two
electrons localized on the same impurity (as a result of a large lattice relaxation).
It is now generally accepted that the model proposed by Chadi and
Chang in 1988 [Chadi88] is the correct one. One modification to this original
model, referred to as the Chadi-Chang model (or CCM), is the idea proposed
by Yamaguchi et al. [Yamaguchi90] that, in addition to the ground state with
large relaxation, the DX center has also a metastable resonant state with small
lattice relaxation and symmetry A1. The existence of this state which is neutral
rather than negatively charged has now been confirmed by several theoretical
calculations [Dabrowski92] and experiments [Suski94].
The CCM which used the approach based on a super-cell self-consistent pseudopotential
calculation has two important features:
1. When the DX center becomes the stable ground state of the substitutional
donor impurity in GaAs or AlGaAs (as a result of either high pressure or
alloying), the DX center is formed by one neutral donor capturing an electron
from another neutral donor atom. This process can be represented by the
“reaction”:
2d 0 → d DX
where d 0 and d represent, respectively, a fourfold-coordinated substitutional
donors in the neutral and ionized state. The resultant DX center is negatively
charged and contains two electrons localized on the same donor atom. Normally
two electrons will repel each other via the Coulomb interaction U (see
4.3, p. 182). In special cases, such as encountered in the DX center, two electrons
can attract each other as a result of electron-lattice interaction. Such
defect centers exhibiting attractive Coulomb interaction between electrons are
referred to as negative-U centers [Baraff80].
2. The DX defect formation involves a large bond-rupturing displacement of
either the defect atom or the host lattice atoms. For donors on cation sites,
such as SiGa, the donor atom is displaced as shown in Figs. A4.6(a) and (b).
In the case of donors located on anion sites, such as SAs, one of its nearestneighbor
Ga (or Al) atoms along a bond axes, is displaced. This is illustrated
in Figs. A4.6(c) and (d). Thus the local symmetry of a donor is charge dependent.
When the electron occupancy of the donor is 0 or 1, corresponding to
the positively charged d or neutrally charged d 0 states, the local symmetry of
the donor in the vicinity of the donor atom is tetrahedral (i.e., the point group
symmetry is Td) and there is no lattice relaxation. When the electron occupancy
is increased to 2, corresponding to the negatively charged DX state,
the defect symmetry is lowered to trigonal (the point group symmetry is C3v)
as a result of a bond-breaking lattice relaxation.
The reason why a deep and localized state becomes favorable in GaAs
under pressure or alloying with Al is the near degeneracy between the three
conduction minima at °, L and X. The contribution of all these conduction
minima to the deep DX state manifests itself in its alloy and pressure dependence.
Instead of following either the °, L or X conduction valleys as a func-