Exercise n°2

For an abrupt PN junction, the dopant concentration varies suddenly from NA to ND. The following figure gives the charge, electric field and electrical potential distributions inside the depletion zone.

The electric field is given by :

This relationship shows that the depletion zone is more extended in the lowest-doped side.

The diffusion voltage is given by:

The width of the depletion zone is :

w =xn + xp but we have shown in a) the following relationship : NAxp = NDxn

Hence :

so that :

Furthermore, the electrostatic potential is related to the charge distribution by :

It is then possible to derive the expression for the diffusion voltage :

Since :

we get :

The depletion zone width is then :

Numerical application :