Applying a voltage across the Depletion Zone the Fermi Energy ( EF ) no longer lines up.
Figure 16.1 - Applying a Voltage Across the Depletion Zone
The barrier height, when a voltage is applied, changes from Vbi to Vbi-Vapplied
16.2 Analysis of I-V Characteristics
Now (at the edges) of the Depletion Zone, the carrier concentrations are related by
pn
pp
=
np
nn
=e
-
e(Vbi-Vapplied)
kT
from this we see that we have changed from the equilibrium values pn0 and pp0 (??where the 0 represents the thermal value??) by a factor of
pn
pn0
=
np
np0
=e
eVapplied
kT
this results in changes in the carrier concentration to be
D pnº (pn-pn0)=pn
æ ç ç ç è
e
-
eVapplied
kT
-1
ö ÷ ÷ ÷ ø
this is similar for electrons.
Figure 16.2 - Changes in the Carrier Concentration (No Applied Voltage)
Figure 16.3 - Changes in the Carrier Concentration (Forward Bias)
In the region next to the Depletion Zone, the injection of carriers mean that np>>ni2 which makes the system out of equilibrium. The injection of carriers can result in two outcomes
the combination which results in the possible emission of light in the time trecombine
the can diffuse down the concentration gradient
This results in the exponential decaying profile
D n(x)=D npe
-
x
Le
where L is the Diffusion Length, Le=Detrecombine . Le is a measurement of how far the electrons will get before they recombine.
