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figure, the anti-bonding level approaches the isolated hydrogen atom self-
energy,
E
H
,asthe
X
atom electronegativity increases (
E
X
decreases). On
the lower right-hand side, the bonding level approaches
E
H
, from below,
as
E
X
increases and the
X
atom becomes significantly less electronegative
than the H atom. In summary, as
|
−
|
, and the electronegativity dif-
ference increases, one of the energy levels always approaches the isolated
hydrogen atom self-energy,
E
H
.
We can now apply the same picture to a tetrahedral semiconductor,
where the host atom electronegativity is fixed (as was
E
H
above) while
the impurity electronegativity depends on the impurity considered. In
semiconductors, the bonding and anti-bonding levels have broadened
into bands. For sufficiently large electronegativity difference, the defect-
associated state can lie in the band gap, giving a deep level, as illustrated by
the thick solid lines in fig. 4.7(b), while for smaller electronegativity differ-
ences the defect states will lie in the bands, as indicated by the dashed lines.
Such defect-related levels in the bands are referred to as 'resonant' levels.
Because the resonant level is degenerate with the conduction or valence
band, an electron will not remain bound in such a level but can instead
escape into the extended band states. Hydrostatic pressure can be a very
useful tool to study impurity states. The
E
H
E
X
conduction band edge shifts
upwards with pressure, and can thereby induce transitions from resonant
to deep states, as for example with Si donors in GaAs. Such transitions can
also be observed in semiconductor alloys as a function of alloy composi-
tion: Si is a resonant state in Al
x
Ga
1
−
x
As for
x
<
0.2, but becomes deep at
higher aluminium compositions.
C
Conduction band edge
Si
P
As
Sb
Bi
0.2
Substitutional donors
At
0.4
I
Se
N
Se
S
0.6
Experiment
Theory
S
N
0.8
Br
Cl
1.0
Valence band edge
O
-12
-8
s Central-cell potential (eV)
-4
0
Figure 4.8
Comparison of calculated and experimentally determined defect energy
levels for a range of substitutional donors in Si (figure after Vogl, © 1984
by Academic Press, reproduced by permission).
