Classification of metals insulators and semiconductors on the basis of the band theory:
The postition of the two highest bands, their electro occupation and the seperation between their energy levels determination the conductivity of a solit.
The band occupied by the outer, or valence electrons is called the vaIence band. The next allowed band is called the conduction band. Thus, a conductor is a solid whose valence band is only partly or whose conduction band overlaps its valence band.
(a) Conductors:
(i) In a metal, the conduction electrons are force to move throughout the volume of the sample like the molecules of a gas in a close container. In a metal the highest occupiey energy level falls near the middle of an energy band. when a potential difference is applied across a metal, electrons can jump to available vacant levels at nearby higher energies. Conductivity of electricity is possible in metals because electrons in its highest occupied a band can easily move into higher energy levels within that band.
(ii) Mg ( 1s2, 2s2 2p6,3s2)- It has two 3s electrons so the 3s band is filled.However, like Na, the empty 3p band overlaps the 3s band, so Mg is also a conductor.
(iii) Zn (1s2,2s2 2p6 ,3s6 3d10,4s2)- In this case 4p band overlaps with 4s band, so Zn is good conductor.
(b) Insulators -(i) A solid issaid to be an insulator if no current exists within it when we apply a potential difference across it. A current can exist in the solid if some electrons can be transferred to a higher energy level. In insulators the highest band is completely filed and according to pauli exclusion principle electrons can not move from occupied levels. A solid with completely filled valence band is an insulator is'the energy gap between the valence band and the empty conduction band is longer than about 2eV in fig (III).
Although there are vacant levels in the and avove the filled Land, electrons must aoquine enough energy to jump across the substantial energy gap that separates the two bands. In diamod, this gap is 5.5 ev, about 140 times the average thermal energy of a free particle at room temperature hence no electron can jump across it.Thus diamond is an insulator
(ii) Ionic crystals (Na+ Cl-) are insulators.
(iii) Good insulators have enormous resistivity compared to metal (a factor of 1024 greater) most outer shell electrons in an insulators insulators are not free but are involved in ionic or covalent bonds.
(c) semi-Conductors-(i) There are a few elements like Sb, As, Bi,whose conduction band overlaps the valence band only very slightly, limiting the number of available empty state.
These materials are called semimetals.
(ii) Cu has for more charge carriers per unit volume then Si, by a factor of about 1013,For Cu, each atom contributes one electron, its single valence electron, to the conduction process
(iii) The band structure of a semiconductor is like that of an insulator. The main difference is that the semiconductor has a much smaller energy gap Eg between the top of the highest filled band (called the valence band) and the bottom of the vacant band just above it (called the conduction band).
Thus Si (Eg = 1.1 eV) is a semiconductor and diamond (Eg = 5.5 eV) is an insulator. the si thermal agitation at room temperature will cause electrons to jump the gap from the valence band to the conduction band.
