On the definition of voltage and the relationship between internal and external voltages of a semiconductor device

The voltage between two points is the line integral of the electric field between the two points. The voltage between the metal contacts defining two terminals of a device is also the difference between the quasi-Fermi level at the terminals. However, the voltage between two points internal to an isothermal semiconductor device is not necessarily the difference between quasi-Fermi levels. Rather, the voltage involves both quasi-Fermi level and chemical potential differences. An example of a device having ideal ohmic contacts illustrates these points. The results and their application pertain to semiconductor device analysis.