Change of chemical Potential in forward biased pn-junction I asked a more general Question before, in whiches answer this question arose:
If you look at this picture (I have similar pictures in my books on the topic, where they evade the question): 
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(where I assume $E_{Fn}$ and $E_{Fp}$ to be meant as the (quasi-) chemical potential of the holes and the electrons in that point). In b) there is drawn a plot of $E_{Fn}$, and it is curved (obviously because of the influence of a applied potential). $E_{Fn}$ is curved in such a way, that its values far in the n and far in the p-Region differ exactly by the the applied potential difference between the two regions (That means, applying a voltage V shifts the chemical potential at one end of the pn-junction by an Energy eV). 
I want to know why the chemical potential $E_{Fn}$ is shifted exactly(!) like that? Is there any quasi-equilibrium-condition that forces it to do so? In what region is this condition valid? What theory describes this behaviour? Is has to be some theory that makes statements about chemical potentials, but it isn't thermodynamic, which just makes statements about thermodynamic equilibrium (this junction is not in equilibrium). 
 A: The total chemical potential of an electron system (which includes electrostatic potential), also called electrochemical potential or Fermi level, represents the energy you need to add an electron to the system in thermal equilibrium including work performed in electrostatic fields. Therefore, when you apply an electrical potential difference to two isolated bodies (like a p- and an n-y type semiconductor), each in thermal equilibrium, the electrochemical potential of the semiconductors will differ just by this voltage.This situation occurs when you apply a voltage to a pn-junction and you can assume that the p- and n- regions are still approximately in equilibrium and therefore still possess an electrochemical potential. This is the reason why the quasi-electrochemical potentials are shifted exactly by the applied voltage. Then one speaks of local equilibrium and local electrochemical potential (or quasi-electrochemical potential). This local quasi-Fermi level concept is often extended to local electron and holes quasi-Fermi levels in semiconductor devices with applied voltages and currents that are as a whole not in thermal equilibrium. These quasi-Fermi levels for electrons and holes are, in general, different and their slope corresponds to the local diffusion+drift current. Applying zero voltage means that the two semiconductors are in thermal equilibrium and have the same electrochemical potential (Fermi level) which, due to the difference in (non-total) internal chemical potentials, in general, produces an electrical potential difference called contact potential. This equilibrium potential difference, however, seen in pn-junctions, cannot be measured with a voltmeter because there is no difference in electrochemical potential between the n- and the p-region. 
