The quasi-Fermi potential is used to calculate the local
concentration of the considered carrier type. Each segment has a quasi-Fermi
potential of its own which is determined by some contact.
The advantage is that no
continuity equation needs to be solved for this carrier system which reduces
the simulation time. In case of a drift-diffusion equation set, the equation
system size is reduced by about 1/3. In case of a hydrodynamic simulation
the reduction of the equation system size is about 2/5 since the
corresponding continuity equations and the energy flux equation are not solved,
such that a five equation system reduces to a three equation system.
This reference potential is then used to calculate the carrier concentrations
in the respective segments. An example is an n-channel MOSFET, for which the
holes in the substrate represent the minority carrier system. Since they contribute
only marginally to the drain current, it is in many situations justified to ignore
the hole current at all by assuming a constant quasi-Fermi level. The
equations for the electron and hole concentration read
n | = | N_{C}^{ . }exp - | (3.19) |
p | = | N_{V}^{ . }exp . | (3.20) |