JEE Main & Advanced Physics Semiconducting Devices Conductivity of Semiconductor

(1) In intrinsic semiconductors \[{{n}_{e}}={{n}_{h}}\]. Both electron and holes contributes in current conduction.

(2) When some potential difference is applied across a piece of intrinsic semiconductor current flows in it due to both electron and holes i.e. \[i={{i}_{e}}+{{i}_{h}}\Rightarrow i=eA[{{n}_{e}}{{\upsilon }_{e}}+{{n}_{h}}{{\upsilon }_{h}}]\]

(3) As we know \[\sigma =\frac{J}{E}=\frac{i}{AE}\]. Hence conductivity of semiconductor \[\sigma =e[{{n}_{e}}{{\mu }_{e}}+{{n}_{h}}{{\mu }_{h}}]\]; where \[{{v}_{e}}=\] drift velocity of electron, \[{{v}_{h}}=\] drift velocity of holes, E = Applied electric field \[{{\mu }_{e}}=\frac{{{v}_{e}}}{E}=\] mobility of electron and \[{{\mu }_{h}}=\frac{{{v}_{h}}}{E}=\] mobility of holes

(4) Motion of electrons in the conduction band and of holes the valence band under the action of electric field is shown below

(5) At absolute zero temperature (0 K) conduction band of semiconductor is completely empty i.e. \[\sigma =0\]. Hence the  semiconductor behaves as an insulator.