• While it is possible to apply Nernst-Einstein's relation to express the motions of both ions and electrons to state the similarity between electrons and ions, in reality the motion of electrons is quite different.
  
  

• In metals, semiconductors and high mobility ceramics, the electrons and holes are considered as quasi-free particles with a drift velocity, v_d , acquired under an applied electric field. The extent of this drift velocity is governed by various scattering phenomenon such as scattering from the lattice.

Under an applied field E, the force on an electron is given as

	(3.34)

In such a condition, drift velocity increases in such a manner as expressed by Newton's law of motion:

	(3.35)

where m is the mass of carrier, v is velocity and t is the relaxation time.

Under steady-state conditions i.e. when carrier motion reaches a steady state,

	(3.36)

and hence mobility, μ, can be defined as

	(3.37)

where m^* is the effective mass of the carrier. Typically, in metals and semiconductors, the relaxation time, τ, shows a temperature dependence and varies as T^-3/2 due to thermal scattering and T^3/5 due to impurity scattering. For details, please consult any book on the basic solid state physics as mentioned in the Bibliography.