When we form a junction of p-type silicon and n-type silicon there will be a flow of charge across the junction in order to equalise the Fermi levels. The excess electrons will flow from the n-type to the p-type and the excess holes from the p-type to the n-type material until the Fermi levels are equalised .
At equilibrium an equal number of electrons and holes will flow in unit time in opposite directions across the pn junction.
The flow of charge across the junction will produce a barrier as a result of the space charge layer or depletion layer.
The amount of charge that flows across the junction in order to equalise the Fermi levels is quite small (of the order of 10- 13 C mm-2)
We can relate the barrier height or potential difference across the junction to the charge transferred and the density of dopants in the p and n layers.
By solving Poisson's equation for the pn junction we find that
where
Q= charge transferred across the junction,
Na= density of acceptors in the p-type material,
Nd = density of donors in the n-type material.
The width of the depletion region (barrier region) is the sum of the p-type depletion width lp and the n-type depletion width ln. It is found from:
or 
Thus the relative widths of the depletion regions are inversely proportional to the densities of carriers on each side of the junction.
The height of the barrier depends directly on the charge density ? .