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It should be noted that < EF. This does not limit the applicability of ( N was calculated for simplicity for 6.11), however, since the T ! If the highest filled s-band of a crystal is occupied by two electrons per atom, i.e., if the band is completely filled, we would expect that the electrons cannot drift through the crystal when an external electric field is applied (as it is similarly impossible to move a car in a completely occupied parking lot).6.6.6.7(a)).6.7(b)).

It should be noted that
< EF. This does not limit the applicability of (
N was calculated for simplicity for
6.11), however, since the
T ! 0 and
number of electrons does not change when the temperature is increased. In
other words, integrating from zero to infinity and using T 6¼ 0 would yield
essentially the same result as above.
6.6. Consequences of the Band Model
We mentioned in Section 6.4 that, because of the Pauli principle, each
s-band of a crystal, consisting of N atoms, has space for 2N electrons, i.e.,
for two electrons per atom. If the highest filled s-band of a crystal is
occupied by two electrons per atom, i.e., if the band is completely filled,
we would expect that the electrons cannot drift through the crystal when an
external electric field is applied (as it is similarly impossible to move a car in
a completely occupied parking lot). An electron has to absorb energy in
order to move. Keep in mind that for a completely occupied band higher
energy states are not allowed. (We exclude the possibility of electron jumps
into higher bands.) Solids in which the highest filled band is completely
occupied by electrons are, therefore, insulators (Fig. 6.7(a)).
In solids with one valence electron per atom (e.g., alkali metals) the
valence band is essentially half-filled. An electron drift upon application of
an external field is possible; the crystal shows metallic behavior (Fig. 6.7(b)).
Bivalent metals should be insulators according to this consideration,
which is not the case. The reason for this lies in the fact that the upper