We have seen how n (and p) doping raises (lowers) the Fermi energy. What happends at a junction between materials of opposite types? If we draw together the ideas we have explored on drift, diffusion, Laws of Mass Action and Doping Statistics we can answer this question.
15.2 p-n Junctions in Thermal Equilibrium
EF is a constant throughout the device and there is no net flux of either electrons or holes. A long distance from the junction EF must be in the same position as it is for a bulk doped crystal.
Figure 15.1 - A p-n Junction
Imagine bringing the p-doped and n-doped materials togethers so that they are in contact with one another, the electrons flow from the n-type to the p-type material. This leaves equal charge densities on either side of the junction. This establishes a built in voltage ( Vbi ) which is typically a little less than Eg .
15.3 The Electrostatics of p-n Junctions
Figure 15.2 - Electrostatics of a p-n Junction (On Handout 9)
Vbi is only typically close to Egprovided that the doping levels are reasonably high. At the junction there is a region called the Depletion Zone which is devoid of free carriers. For both carrier types a drift current exists in one direction so that it exactly balances by the diffusion current in the opposite direction. The carrier concentrations on either side of the junction are related to the Boltzmann factor.
pn
pp
=
np
nn
=e
-
eVbi
kT
where pn is the hole concentration in the n-type material and pp is the hole concentration in the p-type material.
