# BAND STRUCTURE and SEMICONDUCTORS - 3H

### We need to start with a few slides containing some additional material that
is needed for this section; here.

Let us take a system of N electrons with a distance a between the atoms and a
total length of L. We can calculate that if each atom has Z electrons
contributing to the gas of electrons, then there are N=Z(L/a) electrons. The
momentum, P_{F}, at the Fermi Energy E_{F} is equal to (pi/2a)Z.
In a metal with one free electron per atom P_{F} =(pi/2a) and the band
would be partly filled and so conduction could easily occur and would be
strongest at a low temperature.

In another solid, possibly a semiconductor that has 2 electrons in the
external shell, the momentum at the Fermi Energy would be P_{F} =(pi/a).
There would be a gap, Delta, between the end of this band and the next level,
but if this was small then there would be the possibility that as the
temperature was increased, some electrons would jump up over the gap. Conduction
here increases as the temperature increases because hot electrons move around
more than cold ones do.

The bands introduced above have names that describe their functions:

### This section was added on 16/12/03.

The energy gap of an insulator is at least 5eV and aften more like 10eV. Band
gaps in intrinsic semiconductors are of the order of 1eV and can reach up to 4eV
or thereabouts.

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