10. Appendix

682 Appendix C
tion of alloying (see Fig. A4.4) or pressure, the deep DX state roughly follows
an average (weighted by the degeneracy of each kind of valley) of the dependence
of all the valleys. Because of this degeneracy in reciprocal space, itis
energetically favorable for the electron wave function to become delocalized
in reciprocal space while becoming localized in real space. This localization is
achieved via a large lattice distortion. In other words, the defect electron can
lower its energy by “trading-off” lattice energy with electronic energy. In order
to maximize the gain in electronic energy the DX center attracts an extra
electron when it undergoes lattice relaxation so that the total gain in electronic
energy is doubled while the lattice energy spent remains the same. The idea
that the DX center may be a negative-U center was proposed independently
by Khachaturyan et al. [Khachaturyan89].
Fig. A4.6 The displacement of the donor atoms or
the surrounding host atoms in forming the DX center.
In (a) and (c) the substitutional atoms are in
their neutral states and located in tetrahedral sites.
In (b) the substitutional Si atom is shown displaced
along one of the Si-As bonds into a site where it is
surrounded by only three As atoms. In (d) the substitutional
S atom is not displaced but, instead, one
of its three Ga neighbors is relaxed in a pattern
similar to the Si donor in (b). Reproduced from
[Chadi88].
A4.1.5 Experimental Evidence in Support of the Chadi-Chang Model
The CCM was not immediately accepted because initial attempts to measure
the large lattice relaxation associated with the DX center turned out
to be quite difficult. On one hand, it was possible to introduce only around
10 18 cm 3 of such centers. Techniques for measuring lattice displacements such
as x-ray diffraction and extended x-ray absorption fine structures (or EXAFS)
are not sensitive enough for low atomic number atoms like Si. Heavier atoms,
like Sn, induce smaller lattice displacements. On the other hand, measurement
of the -U properties of the DX centers was easier and the correctness of the
CCM became accepted based on its correct prediction of the properties of the
DX centers including their -U nature.
The -U nature of the DX centers has now been established by several experiments.
Perhaps the most convincing ones are those based on the concept
of co-doping. As we noted earlier, most DX centers exhibit similar properties,