Differentiate between extrinsic and intrinsic semiconductor. Obtain an expression for the carrier concentration for an intrinsic semi-conductor. Also demonstrate that Fermi level in an intrinsic semiconductor lies approximately half way between the top of valence band and the bottom of conduction band.

In intrinsic semiconductors, conduction is because of intrinsic processes characteristics of crystal, without influence of impurities. A pure crystal of silicon or germanium is an intrinsic semiconductor. Electrons which are excited from the top of the valence band to the bottom of the conduction band by thermal energy are responsible for conduction. Number of electrons excited across the gap can be calculated from the Fermi-Dirac probability distribution. In extrinsic semiconductors, conduction is because of the presence of extraneous impurities.  Process of deliberate addition of controlled quantities of impurities to a pure semiconductor is known as doping. Addition of impurities markedly increases the conductivity of a semiconductor. Conductivity  of  an  intrinsic semiconductor  depends  on  concentration  of  charge  carriers,  n_e and  n_h.  Mobility  of conduction electrons  and  holes  µe and  µh can  be  defined  as  drift  velocity  acquired  by them  under  unit  field  gradient.  The conductivity σ of a semiconductor can be written