Exploring Diffusion & Drift in a Zero-Bias PN Junction

[saubhik]

consider we have a pn junction in zero bias. I am trying to find the equilibrium condition.

As soon as a p-n junction is formed, electrons (present in conduction band) from the n-side near to the p-n interface diffuse to the p-side of the interface leaving donors in the region. Same thing happens for holes (present in valence band) which diffuse from the p-side near the interface to the n-side; leaving acceptors in the region. this results in thermally-induced diffusion current, which results from the random Brownian motion of charge carriers independent of electrical stimulus.
Here arises a question: After sufficient diffusions, is the number density of holes and electrons constant throughout?Is diffusion restricted to space charge region? I assumed it so. (since i think, if diffusion did spread the carriers all over ,the neutral regions of n,p-side would lose their neutrality.

So now we have a space charge region aka depletion region where there are fixed donor ions in the n-side and fixed acceptor ions in the p-side of the interface. Beyond this region there is neutral region in both sides. Gradually an electric field sets up due to the space charges which opposes the diffusion.The electric field due to the space charges exist only in the space charge region. This opposes the further diffusion when the depletion region has gained sufficient width.

Please check this reasoning: The diffusion and drift is limited only within the space charge region at equilibrium. Before attaining equilibrium the diffusion being stronger increased the width of the depletion region.The diffusion force did not send the carriers out of the space charge region at any instant. Thus no electron from n-side wanders over the neutral region of p-side due to diffusion and consequently for holes. With increase in width and fixed charges surrounding the interface, the electric field increased. At certain instant, drift current and diffusion current equals each, attaining equilibrium.

This diffusion and drift takes place simultaneously and at equilibrium diffusion current equals drift current. Both currents have completely different origin: one is thermally induced another is electrically stimulated.

I am confused. Please help.

 

[jbsteele]

The equilibrium condition for a pn junction in zero bias is that the diffusion current and drift current are equal. This means that the diffusion of charge carriers (electrons and holes) and their drift due to the electric field created by the space charges in the depletion region are equal. At equilibrium, the diffusion force has increased the width of the depletion region enough so that the electric field created by the space charges is strong enough to counteract the diffusion force and create an equilibrium condition. There is no further net movement of charge carriers beyond the space charge region at equilibrium.