Carrier motion in a chemical potential gradient

The most general way to express the force, F, on a particle is through the corresponding gradient in the chemical potential, p  

Note keeping as elose to the standard symbols used by the community as possible leads to some confusingly similar symbols. Here p is the electron mobility and p (no subscript) is the chemical potential (of the electron). Electron chemical potential gradients may result from many factors, but for the current discussion, we will consider only electric fields and concentration gradients. The presence of an electric 

Likewise, a change in electron concentration, n, in the absence of an electric field causes a change in chemical potential  

Therefore, the general chemical potential gradient in the system is given by 

The second term on the right side of Equation 3.5 is the electric field. Substituting for chemical potential gradient in Equation 3.2 gives  

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