Text_Template

Module 4 : Solid State Chemistry

Lecture 20 : Band Theory of Solids

When metals with a band occupancy as in Fig 20.4 are subjected to an external electric field, the electrons are highly mobile and flow "almost freely" in the band leading to high electrical conductivity.

Let us next consider the energy bands in semiconductors, shown in Fig 20.5. Here too, at T = 0K, the valence band is completely filled and the upper or the conduction band is empty and the conductivity is negligible. This is similar to diamond except that the gap between the occupied valence band and the higher unoccupied conduction band is small. As the temperature is increased, some levels of the higher band get occupied due to thermal excitation and the system behaves as a conductor. This is observed in the case of elements like Ge and Si and they are called semiconductors. These materials exhibit increased conductivity with increasing temperature.

Figure 20.5 The band structure of a semiconductor.

Another way of getting semiconducting behaviour is to "dope" pure materials with foreign atoms (dopants) which are either rich in electrons ( i.e., atoms that can donate electrons) or are short of electrons ( i.e., these atoms can trap electrons). For example, when phosphorus is doped into germanium, the additional electrons in P (the donor band) can occupy the empty conduction band in Ge heading to conducting behaviour. This is called an n-type semiconductor. On the other hand, if germanium or Si is doped with electron "deficient" materials such as Al, the band of the dopant can accept electrons from the valence band of the host. Since the band loses electrons, the charge carriers in the valence band are "positive charges" or "holes". This is referred to as p- type of semiconductivity. In n-type, the charge carriers are negative. The band structures of n- type and p-type semiconductors are shown in Fig 20.6

Figure 20.6 The band structures of n-type and p-type semiconductors