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Why is Fermi level referred to as electrochemical potential

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    Arash Hazeghi

    chemical potential has a neat thermodynamical definition, the chemical potential associated with the ith species is the contribution to the internal energy of the system from the ith specie when volume, entropy and other species are kept constant. In particle physics chemical potential is used to describe the distribution of electrons which at thermal equilibrium, have a Fermi-Dirac distribution. On the other hand, in solid state physics, Fermi level is referred to as the the highest energy level occupied in the ground state of an N electron system at 0K. when temperature increases electrons are excited to higher energies and will have a Fermi-Dirac distribution. some books in Electrical Engineering choose to call the chemical potential in the F-D distribution the “Fermi level” however it should be noted that this is no longer the last energy level occupied but a potential with which electrons are in thermal equilibrium. This potential might even be imposed on the system from outside and is not necessarily a sole property of the system alone. It should be noted that there is no Fermi level or single chemical potential at non-equilibrium situations such as carrier transport.

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    Suseendran Jayachandran

    Ef=µ=µc+qΘ.This is the expression for the electrochemical potential which is same as the Fermi level. Now if we consider a p-n junction, where the holes from p side move to the n side, and electrons from n side move to the p side. This occurs due to the difference the chemical potential (concentration gradient). While these carriers move, they leave back ions, which gives the intrinsic E field that opposes the movement of these carriers. This intrinsic field is qΘ. Now, the equilibrium is attained, when both the above process becomes equal. (i.e) when their electrochemical potential is same. Thus at equilibrium we name this electrochemical potential as the fermi level to indicate the equilibrium distribution of the carriers.

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