176 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES
Minority carrier concentrationPn=0pn0slopePn=0SlopeΔpn=pn 0 ()eeV/kBT− 1
Figure 4.18: left: Reverse bias minority carrier concentration. right: Forward bias minority
carrier concentration
with each set of traps constituting a separate system. Each of these systems will be represented
by their own quasi Fermi level, EFnfor the electrons, EFpfor the holes and EFTifor the traps
of energy ETi. If thermal energy is the only energy source determining the occupancy of the
different states and the systems are all freely interacting then of course all the quasi Fermi levels
merge into the Fermi level of the system at equilibrium. We have also seen in figure 4.5 that
the quasi Fermi levels vary across a device in non-equilibrium. The variation of the Fermi level
is determined by the current flow in the system and the interaction of the various systems. Let
us look at the variation of EFnand EFpin the case of a forward biased diode in figure 4.5c.
The electron quasi Fermi level is determined by the electron concentration point by point and is
determined by the level set by the reservoir of electrons which is then−type layer. The large
electron concentration in then−type layer ensures that only a small gradient in EFncan sus-
tain current of relevant magnitudes and hence is pictured flat in the bulk. The same applies for
EFpon thep−side. As electrons and holes flow across the depletion region the quasi Fermi
levels remain almost flat because the length of the depletion region is very small allowing large
gradients to be present to satisfy needed current flow with low absolute values ofΔEFnand
ΔEFp. In the depletion region, since there is no recombination assumed, the electron concen-
tration is determined by then−region and the hole concentration by thep−region, and in both
instances substantially by the thermal supply as given by the Boltzmann distribution as shown
in figure 4.6. However, in the bulk regions the electrons and holes recombine and hence the EFn
in thep−region decreases in a manner determined by the recombination rate and not the Boltz-
mann tail of the majority electrons. In the case of reverse bias (figure 4.5c) the injected electrons
and holes are sourced as thermally generated minority carriers in the bulk regions and swept
across the junction to constitute the reverse saturation current. The quasi-femi levels reflect the
change in the minority carrier concentration in the bulk regions on the application of the reverse
bias. The minority carrier electron concentration at the edge of the depletion region of the p-side
under zero bias isnn 0 exp (−eVbi/kBT)ornp 0. On application of the reverse bias ofVr,the
electron concentration at the junction edge supplied by thermionic emission from the n-side is