Module 4 :  Solid State Chemistry
Lecture 20 : Band Theory of Solids
  20.2

Band structures in insulators, metals and semiconductors

The term band structure refers to the size of various bands, the gap between adjacent bands and the occupation of the levels in the bands by electrons. In the solids formed by systems such as rare gas atoms, all the bands (corresponding to filled shells in atoms ) are completely filled with electrons and the unfilled bands (corresponding unoccupied orbitals in the atoms) are fully empty. There is no discernible movement of these electrons when the system is subjected to an external electric field and the substance behaves as an insulator. The same is true for diamond (Fig 20.3) where the filled bonding sp3 band is widely separated from the unfilled antibonding sp3 by a considerable gap and the substance is a well known insulator.

 
        
 

                                                    Figure 20.3 Filled and unfilled sp3 bands in diamond.

 
In the case of metals such as Li, Na, Mg and Al, the atoms have partially filled shells. The bands in the metals are also partially filled. Consider the case of N electrons occupying a band of N orbitals. Only N / 2 orbitals are occupied and the band is only half full as shown in fig 20.4.
 
        


                                                              Figure 20.4 : Partly filled band in a metal.