drift current:In semiconductors, the charge carriers are electrons in conduction band and holes in valency band. They move randomly in all direction in the absence of electric field. When an electric field E is applied across a semiconductor every charge carriers experiences a force and drift in the direction of field.
definition: The total current due to holes and electrons with the application of electric field is called drift current. In general current density is given by Substituting drift velocity in current density 'J' we get
Current density of the electrons is
Current density of the holes is
The total drift current is the sum of the current density of electrons and holes
In intrinsic semiconductor, all charge carrier are equal
Hence the drift current changes to
By the definition of current density we have
By equating both the current densities, we get
Electrical conductivity of the Intrinsic semiconductor is given by

Diffusion current:In addition to drift current, there is another current called Diffusion current.
In extrinsic semiconductor, the excess charge carriers move from high concentration region to low concentration region. This leads to the current called, Diffusion current. According to the Fick's law of diffusion
In the case of ntype semiconductor, diffusion is due to electrons then,
In ptype semiconductor, the diffusion is due to holes then,
So the total diffusion in a semiconductor is
The total current density J is the sum of Drift current and Diffusion current.
