4.11 Chapter2.2.3;2.2.4;2.2.5;insulator,semi-conductor,metal

2.2.3. distinction between insulator,semi-conductor and metal based on the band theory of solids.

In Figure 2.2.24. the comparative study of the Band-Diagrams of Insulator, Semi-conductors and Metal is given.Close examination of the Band-Diagrams reveal that there is really no difference between Insulator and Semi-conductor except that Insulator has a band-Gap greater than 4eV and within the permissible range of temperatures, electrons can never jump across the band gap into the conduction band and Insulator will always be a bad conductor of electricity. In contrast in Semi-conductors, electrons from the valence band manage to jump across the band-gap right after crossing 77K temperature and at Room Temperature 300K there is appreciable amount of mobile electrons and holes as given in Table 2.2.4.1. Ge, Si and GaAs have intrinsic concentration of 10 ¹³ /cc , 10 ¹⁰ /cc and 10 ⁶ /cc respectively. That is precisely why Ge and Si behave as semi-conductor whereas GaAs behaves as semi-insulator. In contrast Metal always has conducting electrons in Conduction Band. Hence it is a good conductor at all temperatures. All metals have atom packing density of 10 ²² /cc and all metals are univalent hence every atom contributes 1 electron to the conduction band therefore metals in general have n(conducting electron concentration) = 10 ²² /cc. Metals generally have partially filled conduction band or overlapping valence and conduction band as shown in Figure 2.2.25.

There is one very distinctive difference between Semiconductor and Metal. As seen in Figure 2.2.24, Fermi-Level is in the middle of the Band Gap in semi-conductor whereas in Metal Fermi-Level lies in the conduction band and conduction band is filled up with conducting electrons till Fermi-Level.

As we will see later that as we dope a semiconductor, Fermi-level moves towards the Conduction Band in N-Type Semiconductor and towards the Valence Band in P-Type Semiconductor. In heavily doped semiconductors where doping level exceeds Effective Density of States at E _C in case of N-Type material and exceeds Effective Densitty of States at E _V in case of P-Type Semi-conductor then Fermi-level penetrates the Conduction Band N-Type Semiconductor and penetrates Valence Band in P-Type Semiconductor and they are called degenerate semi-conductor. These heavily doped semi-conductors behave like semi-metals.

2.2.4.thermal generation of elecron-hole pair(ehp) in intrinsic semiconductor.

Electronic Grade Semiconductor with no dopents are called Intrinsic Semiconductor. At temperatures below liquid Nitrogen temperature (77K), intrinsic semiconductor freeze out. There are no conducting electrons and no conducting holes. As temperature is raised above 77K, due to thermal vibration of the lattice structure a few covalent bonds break and n _i electrons leave their host atoms and by corollary p _i holes are created in the vacancies left by the semi-free electrons. Broken-loose electrons behave like negatively charged carriers with an effective mass near the mass of a free electron. The vacancies behave like positively charged carriers with effective mass heavier than that of negatively charged carriers. Here by definition the concentration of the two kind of mobile carriers are equal that is: