Important initial work has been carried out by Schlüter er al
[21] at AT&T who demonstrate that the rare-earth impurity
problems can be investigated with pseudopotentials and is then no more
difficult to treat than transition metal impurities. Relativistic
effects are included through a scalar non-local pseudopotential. The
f-electrons were treated as part of the core which allows a proper
description of crystal field and covalency effects but there is a
price to be paid as the oxidation state of the rare-earth needs to be
selected at the outset. Of course, the calculations can be repeated
with different oxidation states but the theory is unable to predict
with confidence the promotion energies between them. Thus there is a
problem in deciding the relative formation energies of different
defects. Schlüter et al got round this problem by assuming that the
energy for promoting a 4f electron to a 5d state is the observed
energy difference between the lowest energy multiplet 4 
multiplet in the atom, and the 4 
multiplet with
lowest energy. They found that the lowest energy state was Er 
at the 
interstitial site, which is almost degenerate with a
substitutional one. This is in agreement with channelling data
[18] and of the splitting of the luminescence by uniaxial
stress [1]. They also were able to explain the stability of
this oxidation state as arising from a rehybridisation effect.
Nevertheless, it is clear that subsequent experimental work requires
Er to be surrounded by O and other light elements. The local
structure then would enable a stronger coupling between the
f-electrons and the ligands and enhance the oscillator strength of
the transition. However, non-radiative transitions are also likely to
be enhanced by the light impurity and this degrades the PL efficiency.
In the absence of clear understanding of the structure of Er in Si,
most theoretical works have concentrated on systems where the RE is
substitutional and stays on-site as in InP:Yb .
Tight-binding theories of these RE impurities have been constructed by
Lannoo and co-workers [24, 25] and Masterov
[26] although these theory cannot account for the
paramagnetic acceptor level 30 meV below 
, seen in DLTS
[12], and a hole trap 50 meV above 
. There is then a need
for a more sophisticated approach - such as that described here- to
investigate the character of any levels.
The excitation mechanism of the 
F 
F
luminescence due to Yb in InP seems well established: a
electron is trapped in the near level of Yb , and the
negative centre subsequently traps a hole as a bound exciton. An
Auger process then leads to the exciton relaxation by exciting
F which subsequently relaxes radiatively to F.
There is also evidence from Zeeman splitting that the frozen core in
inadequate to describe the f-orbital wave-functions. Lannoo finds
that the lifetime of the excited F state (about 6 
s)
is in reasonable agreement with the data but the problem of O-codoping
cannot be considered by this simple theory.