Current:
There are 2 components of current; electron current density 
and hole current density 
. There are a number of mechanisms of current flow:
(1) Drift
(2)Diffusion
(3) Thermionic emission
(4) Tunneling
The last two mechanisms are significant only at the interface of two different materials like a semiconductor-semiconductor junction or a metal-semiconductor junction where the two semiconductors are of different materials. Tunneling is also important in the case of PN junctions where both the sides are heavily doped.
In bulk of the semiconductor, the dominant conduction mechanisms involve drift and diffusion. The current densities because of these two mechanisms can be written as
here 
are electron and hole mobilities respectively and 
are the diffusion constants.
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