- "one could conceive of means to extract work from an equilibrium
situation by emitting electrons and then reabsorbing them an
infinitesimal distance away where E0 had changed value". What does
In physics, the vacuum level refers to the energy of a free stationary electron that is outside of any material (it is in a perfect vacuum). It may be taken as infinitely far away from a solid, or, defined to be near a surface. (a quote from Wikipedia)
In the source you quote, the vacuum level E0 is defined to be near a surface separating a vacuum from materials.
Notice than that a) the energy of a free stationary electron in a vacuum is an electrostatic potential times the electron charge, and b) at the discontinuity of electrostatic potential, the electric field strength is infinite.
Imagine a setup with a horizontal interface separating materials from a vacuum and vertically oriented metal-semiconductor junction.
Now, consider a closed rectangular contour of an infinitesimal (very narrow) width and of a commensurate height. Let its vertical sides cross a material-vacuum interface, and one of its horizontal side, which lies in a vacuum, crosses the electrostatic potential discontinuity. We calculate an electric field circulation, which in this case is expected to be zero (inferred from energy conservation in static fields). Since there is no discontinuity of electrostatic potential in a material (metal and semiconductor pieces are in contact), the electric field strength along the horizontal side in a material is finite and the circulation contribution of the horizontal side lying in a material is proportional to the rectangular width. Since there is no infinite electric field components orthogonal to a material-vacuum interface, the contribution of the vertical sides is proportional to the rectangular height. Decreasing the rectangular dimensions, the contributions of the three sides of the closed rectangular contour can be made arbitrarily small, and therefore they cannot compensate the contribution of the horizontal side lying in a vacuum which tends to a value of the discontinuity divided by the elementary charge value. We arrive at a contradiction, therefore, there cannot exist a vacuum level discontinuity in a setup under consideration.
- Why is only one generic Fermi level for silicon (called Efs)
represented in the picture?
see, for example, https://www.iue.tuwien.ac.at/phd/ayalew/node53.html :
"Obviously, when the excess carrier concentration is small compared to the equilibrium carrier concentration, the quasi-Fermi level must be very close to the Fermi level. For device operation, we often use a low-level injection condition, meaning that while the minority carrier concentration is changed, the majority carrier concentration remains un-affected. Thus the quasi-Fermi level of the majority carrier is the same as the Fermi level."
Notice also that the Schottky diode is a majority carrier device.