Page 147 - Electrical Properties of Materials

Extrinsic semiconductors 129

Table 8.1 Energy levels of donor (group V) and acceptor (group III) impur-
ities in Ge and Si. The energies given are the ionization energies, that is, the
distance of the impurity level from the band edge (in electron volts)

Impurity Ge Si
Donors Antimony (Sb) 0.0096 0.039
Phosphorus (P) 0.0120 0.045
Arsenic (As) 0.0127 0.049
Acceptors Indium (In) 0.0112 0.160
Gallium (Ga) 0.0108 0.065
Boron (B) 0.0104 0.045
Aluminium (Al) 0.0102 0.057

Thus, this model leads to the following estimate:
2 2
∗ 4
E g – E D = m e /8 h . (8.26)
Taking silicon as an example, for which m =0.58m (see Table 8.4) and ε r =12
∗
(see Table 10.1), this energy level is smaller by a factor of 248 than the value
of –13.6 eV given by eqn (4.21) for the hydrogen atom. That comes to 0.0548
eV, not very far from the experimental figures in Table 8.1. Note, however, that
the parameters in eqn (8.26) depend only on the properties of the host material,
so this model cannot possibly say anything on how E g –E D varies with the type
of dopant.
If instead of a group V impurity we had some group III atoms, for example,
indium (In), aluminium (Al), or boron (B), there would be an electron missing
from one of the covalent bonds (see Fig. 8.4). If one electron is missing, there
must be a hole present.
Before going further, let me say a few words about holes. You might have
been slightly confused by our rather inconsistent references to them. To clear
this point—there are three equivalent representations of holes, and you can
always (or nearly always) look at them in the manner most convenient under
the circumstances.
You may think of a hole as a full-blooded positive particle moving around
in the crystal, or as an electron missing from the top of the valence band, or
as the actual physical absence of an electron from a place where it would be
desirable to have one.

E
4 g
Fig. 8.4
(a) In the case of a group III impurity
one bonding electron is missing—
4 3 4 there is a ‘hole’ which any valence
electron with a little surplus energy
E
A
can fall into. (b) This shows in the
4 0 band representation as an acceptor
level just above the valence
) a ( ) b ( band edge.