In equilibrium, there is only one independent variable out of the three variables :
If one of them is known, all the rest can be computed from the equations listed above. We shall
take this independent variable to be potential.
The analysis problem in equilibrium is therefore determination of potential or equivalently,
energy band diagram of the semiconductor device.
This is the reason why we begin discussions of all semiconductor devices with a sketch of its
energy band diagram in equilibrium.
Energy Band Diagram
This diagram in qualitative form is sketched by following the following procedure:
1. The semiconductor device is imagined to be formed by bringing together the various
distinct semiconductor layers, metals or insulators of which it is composed. The starting
point is therefore the energy band diagram of all the constituent layers.
2. The band diagram of the composite device is sketched using the fact that after
equilibrium, the Fermi energy is the same everywhere in the system. The equalization of
the Fermi energy is accompanied with transfer of electrons from regions of higher Fermi
energy to region of lower Fermi energy and viceversa for holes.
3. The redistribution of charges results in electric field and creation of potential barriers in
the system. These effects however are confined only close to the interface between the
layers. The regions which are far from the interface remain as they were before the
Analysis in equilibrium: Solution of Poisson’s Equation with appropriate boundary conditions Non-equilibrium analysis:
The electron and hole densities are no longer related together by the inverse relationship
of Eq. (5) but through complex relationships involving all three variables Y , , p