In electrochemistry, electrolysis for instance, Nernst equation gives the final point of the process. It is determined by the Galvanic potentials of the inactive electorde and the templating metal, temperature, and the activity of the solution/electrolyte. If the inert electrode is semiconductive (i.e. transition metal oxide), I am wondering whether the Galvanic potential is marked by the work function of the material, or whether there is any relationships between the two properties of the material.
Regardless of the material, the work function is the the difference in energy of an electron between vacuum level and the Fermi level. The Fermi level is indeed the same as the electrochemical potential of the electron in the solid. Since the Nernst equation does nothing else but defining how this potential, E, shifts with respect to E(0), i.e. the electrode potential under standard conditions, it is a direct measure for how the work function changes upon polarization of the electrode. The problem is that different energy scales are used. The work function and Fermi level are usually defined against the vacuum level, while the electrode potential or redox potentials in electrochemistry are defined against an arbitrary zero, which is the standard hydrogen electrode (SHE). If you can establish the difference between 0V versus SHE and the vacuum level, then the Nernst equation could be used directly to calculate changes in work function. I believe there are several approaches to this, and you can learn more about it if you look up papers that aim to develop an "absolute scale" of redox potentials. I believe Wolfgang Schmickler has done some work on this.
Regardless of the material, the work function is the the difference in energy of an electron between vacuum level and the Fermi level. The Fermi level is indeed the same as the electrochemical potential of the electron in the solid. Since the Nernst equation does nothing else but defining how this potential, E, shifts with respect to E(0), i.e. the electrode potential under standard conditions, it is a direct measure for how the work function changes upon polarization of the electrode. The problem is that different energy scales are used. The work function and Fermi level are usually defined against the vacuum level, while the electrode potential or redox potentials in electrochemistry are defined against an arbitrary zero, which is the standard hydrogen electrode (SHE). If you can establish the difference between 0V versus SHE and the vacuum level, then the Nernst equation could be used directly to calculate changes in work function. I believe there are several approaches to this, and you can learn more about it if you look up papers that aim to develop an "absolute scale" of redox potentials. I believe Wolfgang Schmickler has done some work on this.
You may get information from
Michael Grätzel, Photoelectrochemical cells
Nature 414, 338-344(15 November 2001)
doi:10.1038/35104607
The classical paper on this subject is this:
H. Gerischer and W. Ekardt, Applied Physics Letters 43, 393 (1983); doi: 10.1063/1.94356
In a semiconductor, the work function is sensitive to the doping level at the surface of the semiconductor. Since the doping near the surface can be also be controlled by electric fields, the work function of a semiconductor is also sensitive to the electric field in the vacuum.
You may get information on this subject from
Practical Handbook of Photovoltaics: Fundamentals and Applications
By Augustin Joseph McEvoy, T. Markvart and Luis Castañer
Academic Press, 2012
as far as i know, the electron work function add the interfacial potential between semiconductor and electrolyte equal to the electrochemical potential. the electron work function is relatively simple, because it takes the vacuum as reference. but the electrochemical potential subject to the interfacial condition, it will be complicated.
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