# PN Junction at Equilibrium

Summary:
I am considering a PN junction at equilibrium, and have a couple of questions.
Consider a PN junction doped with say phosphorous on the N side, and Boron on the P side. Initially, there is an opportunity for the electrons just below the N conduction band to drop to the lower available energy states just above the P valence band. This leaves the N side positively charged and the P side negatively charged, forming a depletion region. This means that there will be an electric field pointing in the direction from N to P. Eventually, there will be an equilibrium that is reached, in which case there is no current in the depletion region.

I do not know which of the following explains why there is no current in the depletion region under equilibrium.
1. The electric field causes electrons from the negatively charged P side to flow back to the N type, and in equilibrium this cancels the flow of electrons from N to P. Also, the electric field causes holes to flow from N to P, and this cancels any holes flowing from P to N. The result of these processes is zero net current.
2. There is no current flowing either from N to P or P to N in equilibrium. In equilibrium, the depletion region is essentially an insulator, and while we have an electric field present in the region, the charge is not free to flow.

## Answers and Replies

phyzguy
Science Advisor
(2) is clearly wrong. The holes and electrons are free to move. (1) is closer, but isn't very clearly stated. Exactly which currents cancel? Try drawing a sketch to show the various currents.

unified
phyzguy,

A sketch would include four currents, two from the field (electrons move against the field, holes with the field) and two due to random thermal motions (electrons from P to N, holes from N to P). In equilibrium these effects cancel.

phyzguy
Science Advisor
phyzguy,

A sketch would include four currents, two from the field (electrons move against the field, holes with the field) and two due to random thermal motions (electrons from P to N, holes from N to P). In equilibrium these effects cancel.
Exactly. This is much more clearly stated than your original (1). In semiconductor nomenclature, the currents driven by the electric field are typically called "drift currents" and the currents due to random thermal motions are typically called "diffusion currents". The drift currents obey Ohm's law (J = σE), and the diffusion currents are driven by concentration gradients and obey Fick's law (J=-D∇n).

unified, berkeman and Baluncore