Condensed Matter Physics - Conductors and Semiconductors

Conductors and Semiconductors

Conductors are of four types
    
(i) Superconductors 
    
(ii) Goods conductors
    
(iii) Semiconductors
    
(iv) Bad conductors or insulators

Semiconductors have a unique property that their conductivity increases with rise in temperature. Fig. illustrates how resistivity falls with rise in temperature. This phenomenon can be explained only on the basis of band theory.

The energy bands which are completely filled at OK are called valence bands. The bands with higher energies are called conducting bands. We will refer to valence band as the top most filled band and condition band as, lowest conduction band that is just above the valence band.

Ev is the top most energy of the valence band and Ec is the bottom most energy of the conduction band then Eg = Ec – Ev represents forbidden energy gap

In metals Eg --> 0, that is valence band and conduction band overlap so that a large number of electrons lie in the conduction band.

In semiconductors, Eg ~ 1 eV. At room temperature it is about 1 – 2 per cent filled .At OK semiconductor is a perfect insulator. Fermi level is an imaginary level which lies between valence band and conduction band such that the probability of finding analects on is 50 per cent or ½. At OK Fermi level is the highest filled level. Fermi level is used as reference level. 

Eg (for Ge) = 0.71 eV and Eg (for Si) = 1.12 eV.

In insulators Eg ~ 6 eV, for example diamond has Eg = 6.3 eV. 

Semiconductors are of two types (a) intrinsic (b) extrinsic or doped

In intrinsic semiconductor no impurity from 3rd or 5th group of the periodic table has been added. So that the density of electrons in conduction band is equal to density of holes in valence band that is, n₁ = h₁where n is electron density and h is hole density. (Subscript i stand for intrinsic)

Extrinsic semiconductor is of two types’ p and n types. These are also called doped semiconductors. In p – type majority carriers are holes. Thus, hp > np third group impurity (B, AI, Ga, In) is added to make p- type semiconductor. 

In n – type majority carriers are electrons it is made by doping donor impurity that is impurity from the 5th group of periodic table like P, As, Bi, Sb. Thus nn > hn

In thermal equilibrium condition ne, he = n². (subscript e denotes extrinsic) fig. show energy – band diagram of p and n – type semiconductors in heavily doped p or n – type acceptor or donor impurity level lie in VB and CB respectively.

Conductivity in semiconductors is due to holes and electrons both. Moreover total conduction is due to diffusion and drift currents.

In an intrinsic semiconductor conductivity 

σ = n_eμ_n + h_eμ_n

Where μ_n and μ_n are mobility of electrons and holes respectively.

For n – type semiconductor

Assuming n ≅ ND σ_n = n_eμ_n ~ ND eμ_n

For p – type semiconductor 

Assuming h ≅ NA σ_p = h_eμ_n ~ NA eμ_h 

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