3.25 Sspd_chapter 1_part 11_solid state of matter  (Page 2/5)

1.10.2. SOLID STATE OF MATTER.

With the development of Quantum Mechanics, Band Theory of solid was proposed by Felix Bloch[Appendix XXXXIII]. As already seen in the last section, electrons in a single crystal solid occupy energy bands separated by forbidden zones known as Band Gaps as shown in Figure(1.40) , Figure(1.41) and in Figure(1.49).

The outer band is known as the conduction band and the band just below is valence band. In insulators and semiconductors, the energy band gap between valence and conduction is wide of the order of eV and conduction band is completely empty at low temperatures for both insulators and semiconductors. That is at 77K (liquid Nitrogen temperature) and below, semi-conductor is an insulator. Only near room temperature and by introduction of controlled amount of impurities that semiconductor acquires a certain degree of conductivity. As we will see in semiconductor chapter the effective density of states at the lower edge of conduction band (N _C )

and at the upper edge of the valence band (N _V ) is nearly the same as shown in Table(1.10). This is of the order of 10^ ¹⁹ permissible states per centimeter cube. Hence as soon as doping approaches this order of magnitude, number of conducting electrons are comparable to the available energy states which is the criteria for degenerate systems. Hence at that order of magnitude of doping, semiconductor becomes degenerate and behaves like a semi-metal.

So an INSULATOR can be defined as the solid which has an empty conduction band and a large band gap , of the order of 4eV or more. There electron- hole pair cannot be thermally generated . Hence it remains non-conducting at all temperature.

On the contrary, SEMICONDUCTORS are non conducting and hence insulator below liquid Nitrogen temperature and above liquid Nitrogen temperature they acquire conductivity either due to thermal generation of electron-hole pair or due to contribution of conducting electrons by net donor atoms or due to holes contributed by net acceptor atoms.

Metals have partially filled conduction band or overlapping conduction and valence bands. As a result, there are mobile electrons available in copious amount. This amount is of the order 10 ²² per centimeter cube. As we see in the Table(1.10), atomic concentration in Solids are of the order of 10 ²² per c.c. and each atom contributes an electron for conduction. Hence availability of conduction electrons is 12 orders of magnitude greater than intrinsic Silicon and 9 orders of magnitude greater than that of intrinsic Germanium. Because of this large number of mobile carriers present in metal that resistivity is so much lower in metal than that in semiconductor. This point will become clearer as we proceed with the quantum-mechanical interpretation of conducting electron in metal or in semi-conductor.

As seen in Table(1.10) , the mobility of conducting electrons in semiconductors is much higher than that in metal which is typically 44cm ² /(V-sec) for Copper.

Table(1.10) Characteristics of Ge, Si and GaAs at 300 K.