The substances which contain free charge carrier are called conductors while the substances which do not contain any free charge carrier are called insulators. Semicondcutors are intermediate to conductors and insulators. At NTP a semiconductor behaves as an insulator. The well known examples of semiconductors are germanium (Ge) and Silicon (Si).
The semi-conductors are of two types:
(i) Intrinsic semiconductors : The pure semiconductors are called intrinsic semiconductors. Their conductivity is due to their own (internal) charge carriers. The well known intrinsic semiconductors are germanium (Ge), silicon (Si), i.e., they are tetravalent. The valency of each of Ge and Si is 4.
The bonding between electrons of two neighbouring atoms is covalent, therefore at NTP, there is no free charge carrier for conduction. When a semiconductor is heated, some covalent bonds break due to thermal agitation and thus some electrons get free for conduction. As soon as one electron gets free, there is a deficiency of electrons at its preceding position which acts as a positive charge and is called a hole. The number of holes is equal to the number of free electrons. Thus in an intrinsic semiconductor the conductivity is due to holes and electrons both, which increases with rise of temperature. At normal temperatures only 1 out of covalent bonds break, therefore the conductivity of intrinsic semiconductors is so small, that they cannot be used for practical purpose.
The current in intrinsic semiconductors is of the order of micro amp µA.
In intrinsic semiconductor, the Fermi-level lies at the middle of forbidden energy band.
(ii) Extrinsic semiconductors : If a small amount of trivalent or pentavalent impurity is introduced into a pure germanium (or silicon) crystal, the conductivity of the crystal increases appreciably. Such an impure semiconductor is called extrinsic semiconductor. The conductivity of an extrinsic semiconductor is due to impurities. Extrinsic semi-conductors are of two types :
(a) n–Type (b) p–Type
(a) n-Type semiconductors : When a pentavalent impurity like Phosphorus, Antimony, Arsenic is doped in pure-Germanium (or Silicon), then the conductivity of crystal increases due to surplus electrons and such a crystal is said to be n-type semiconductor, while the impurity atoms are called donors. Thus in n-type semiconductors the charge carriers are negatively charged electrons and the donor level lies near the bottom of the conduction band.
(b) p-Type semiconductors : When a trivalent impurity like Aluminium, Indium, Boron, Gallium etc. is doped in pure Germanium (or silicon), then the conductivity of the crystal increases due to deficiency of electrons, i.e., holes and such a crystal is said to be p–type semiconductor while the impurity atoms are called acceptors. Thus in p–type semiconductors the charge carriers are holes. Acceptor level lies near the top of the valence band.
The conductivity of a semiconductor is
σ = (ne μe + nk μk)
where e is charge on positive or negative charge carrier, ne and n are concentration of electrons and holes, μe and μk are mobilities of electrons and holes.
The mobility (i.e., drift velocity per unit electric field) of holes is less than that of electrons.
Resistivity, (ρ) = 1/conductivity(σ)
Total conduction current due to applied electric field E is
J = σE = e(ne μe + nk μk)E