Set of supplementary notes.

8.2. P-N JUNCTION 109
p
(acceptor-doped)
n
(donor doped)
band scheme
(energy levels)
minority electrons
conduction band
valence band
majority holes
E j
majority electrons
eφ j
minority holes
μ
Mismatch in
chem. pot. μ
causes charge
transfer across
junction, building
contact potential
φ j
. This results
in band bending,
until μ equal on
both sides.
carrier
density
charge
density
electric
field
-eN a
Charge transfer
results in space
Electrons from n-
N a
(acceptor density)
N d
(donor density) side cross
the junction,
annihilate holes
Depletion
from p-side,
layer
causing
carrier-free zone
eN d
(Depletion layer)
charge. Max.
charge density
given by dopant
concentration.
electrostatic
potential
E j
junction
φ j
Space charge
causes in-built
junction field E j
and contact pot.
φ j
, which
build until chargetransfer
stops.
Figure 8.5: Overview of a p-n junction in equilibrium. Far away from the junction, the chemical
potential µ must lie close to the bottom of the conduction band in the n-doped material, and
close to the top of the valence band in the p-doped material. This is achieved by building up
a contact potential φ, which shifts the energy levels as E(z) = E 0 − eφ(z). The change in
potential across the junction is φ j . It gives rise to an in-built field E j .
Potential barrier: The depletion regime of the junction is a high-resistance in comparison
to the n- or p-type doped semiconductors. Any potential across the device is dropped almost
entirely across the depletion layer. The overall potential seen by a (positively charged) hole is
therefore φ j − V , where φ j is the junction potential at equilibrium.
Balance of currents: In equilibrium with no external voltage bias, there is no net current
flowing across the junction. We can, however, distinguish mechanisms which would drive currents
across the barrier in both directions. In equilibrium, these currents cancel. We consider