TABLE OF CONTENTS The MOS transistor needs contact regions, necessarily of a type opposite to that of the substrate, to access the inversion channel. Thus, the modeling of the three-terminal structure or gate-controlled diode of Fig. 2.16 is an intermediate stage in the development of transistor models.
The analysis of the 3-terminal MOS structure combines the MOS capacitor and p-n junction theory, and is conveniently formulated in terms of the quasi-Fermi potentials, the subject of the next section.
The quasi-Fermi potentials 
for holes and 
for electrons are defined in terms of carrier concentrations ( p and n) and potential 
. In order to write the concentrations under non-equilibrium conditions, preserving the form of the Boltzmann equilibrium expressions, one simply replaces the equilibrium Fermi potential with the quasi-Fermi potentials [17] as follows
or
and
In equilibrium, the quasi-Fermi potentials and reduce to the Fermi potential 
. In terms of the quasi-Fermi levels, the current densities are written in a very compact form. For electrons, the total current density in one dimension ( y), including drift and diffusion, is...
