What is the derivation of built in voltage for a P-n junction?

[mertcan]

hi, I am looking a derivation of built in voltage, but the only thing I could find is a statement: built in voltage can be derived from band diagram with the Fermi energy constant throughout the device, or from equating the drift current through the junction equal to the diffusion current. I need some mathematical demonstrations, I tried what the statement had said, but I really lack the mathematical demonstrations for derivation. Could you provide me with proof of it ? Thanks in advance...

 

[CWatters]

Perhaps see second half of this vid..