Equilibrium Fermi Levels
We have observed that the Fermi level must be constant throughout the device at equilibrium. This observation can be easily related to the results of the equilibrium condition.
Since we have assumed that pn and pp are given by their equilibrium values outside the transition region, we can write this equation
in terms of the basic definitions of these quantities using this equ:
Then we get
The Fermi level and valence band energies are written with subscripts to indicate the p side and the n side of the junction.
the energy bands on either side of the junction are separated by the contact potential V0 times the electronic charge q; thus the energy difference Evp - Evn is just qV0.
The above equation results from the fact that the Fermi levels on either side of the junction are equal at equilibrium (EFn — EFp = 0).
When bias is applied to the junction, the potential barrier is raised or lowered from the value of the contact potential, and the Fermi levels on either side of the
junction are shifted with respect to each other by an energy in electron volts numerically equal to the applied voltage in volts.