Classification of solids on the basis of band theory

A solid is determined as a conductor, insulator or semiconductor by the energy band structure.

Conductors

The following figure 11 shows the energy levels and bands in sodium atom (1s2 2s2 2p6 3s1). A sodium atom has a single 3s electron in its valence shell.

 

 

 

Thus if there are N atoms in a solid piece of sodium, its 3s valence band will contain N energy levels can hold 2N electrons. Thus the 3s band in sodium is only half filled by electrons and the Fermi energy EF lies in the middle of the band. When a potential difference is applied across a piece of solid sodium, 3s electrons can pick up additional energy while remaining in their original band. The additional energy is in the form of KE, and the drift of the electrons constitute an electric current. Sodium is therefore a good conductor.

Insulators

In a carbon atom the 2p shell contains only two electrons. Because a p shell can hold six electrons, we might think that carbon is a conductor, just as sodium is. What actually happens is that, although the 2s and 2p bands that form when carbon atom come together overlap as first and the combined band splits into two bands, each able to contain 4N electrons. Because a carbon atom has two 2s and two 2p electrons and in diamond there are 4N electrons that completely fill the lower or valence band. The empty 'conduction band' is above the valance bond separated by a forbidden band 6 eV wide as shown in Fig. (1.12). Here the Fermi energy EF is at the top of the valance band. At least 6eV of additional energy must be provided to an electron to climb to the conduction band. In electric field of over 108 V/m is needed for an electron to gain 6 eV in a typical mean free path of 5x10-8 m. This is billions of times stronger than the field needed for a current to flow in a metal. Diamond is therefore a very poor conductor and is called as an insulator.

 

 

 

 

Semiconductors

Silicon has a crystal structure like diamond; a gap separates the top of its filled valence band from an empty conduction band above it. The band gap in silicon however is only about 1eV wide. At low temperature silicon is little better than diamond as a conductor, but at room temperature a small number of its valence electrons have enough thermal energy to jump the forbidden band and enter the conduction band.

These electrons, though few, are still enough to allow a small amount of current to flow when an electric field is applied. Thus silicon has a resistivity intermediate between those of conductors and those of insulators and is called as semiconductors. The energy band diagram of semiconductor is given in Fig. 13.