Page 146 - Electrical Properties of Materials

128 Semiconductors

8.3 Extrinsic semiconductors
We shall continue to consider silicon as our specific example, but now with
controlled addition of a group V impurity (this refers to column five in the
periodic table of elements) such as, for example, antimony (Sb), arsenic (As),
If the impurity is less than, say, 1 in or phosphorus (P). Each group V atom will replace a silicon atom and use
6
10 silicon atoms, the lattice will up four of its valence electrons for covalent bonding [Fig. 8.3(a)]. There will,
be hardly different from that of a however, be a spare electron. It will no longer be so tightly bound to its nucleus
pure silicon crystal. as in a free group V atom, since the outer shell is now occupied (we might look
at it this way) by eight electrons, the number of electrons in an inert gas; so the
dangling spare electron cannot be very tightly bound. However, the impurity
nucleus still has a net positive charge to distinguish it from its neighbouring
silicon atoms. Hence, we must suppose that the electron still has some affinity
for its parent atom. Let us rephrase this somewhat anthropomorphic picture in
terms of band theory. We have said the energy gap represents the minimum
energy required to ionize a silicon atom by taking one of its valence electrons.
The electron belonging to the impurity atom clearly needs far less energy than
this to become available for conduction. Let us call this energy E imp .Ifan
electron loosely bound to the impurity atom receives an energy E imp it will be
available for conduction, or in other words will be promoted into the conduc-
tion band. If an energy E imp is needed for the promotion then the energy level
of an impurity atom must be below the conduction band by that much, i.e. it
∗
∗ The impurity atom donates an electron. will be at E D = E g – E imp . This energy level is called the donor level. See
Table 8.1 for measured values of E imp .
Interestingly, a very rough model serves to give a quantitative estimate of
the donor levels. Remember, the energy of an electron in a hydrogen atom
[given by eqn (4.18)] is
4
2 2
E =–me /8 h . (8.25)
0
We may now argue that the excess electron of the impurity atom is held by
the excess charge of the impurity nucleus; that is, the situation is like that in
the hydrogen atom, with two minor differences.
1. The dielectric constant of free space should be replaced by the dielectric
constant of the material.
2. The free-electron mass should be replaced by the effective mass of the
electron at the bottom of the conduction band.

4 4 4 E
g
Extra
Fig. 8.3 E
electron D
(a) The extra electron ‘belonging’ to
the group V impurity is much more 4 5 4
weakly bound to its parent atom than
the electrons taking part in the
covalent bond. (b) This is equivalent 4 4 4 0
to a donor level close to the
conduction band in the band
representation. ) a ( ) b (