Lecture 31.03.2003. p-n junction part 1

p-n junction. Diffusion and electrical drift. Dynamical equillibrium. Problems with the sign of current. Current flows against the flow of electrons. Mobility. Fick Law of diffusion similar to Fourier heat conduction. Diffusion driven by density gradient. All inhomogeneity only in x-direction!

Equillibrium. Gives a differential relation for the density and the electric field. Integrate. Obtain the logarithm of density and potential difference. Result: potential difference. This is the potential difference over the p-n junction.

Einstein-Nernst law. Now we assume we know the electric field, constant field. Potential linear. Combine with the Boltzmann factor. This gives the relation for the ratio of diffusion constant and the electric mobility. Put this back to the relation for the potential difference. When kT is expressed in eV (electronvolts) and it is devided by electron charge, we obtain Volts.

Obtain the electron density in the p-doped region from the semiconductor equation (law of mass action). The potential over the p-n junction is related to the density of doping, how many times this is larger than the natural - intrinsic - density of carriers (electrons and holes).

Example: estimate of how large the potential difference can be. Avogadro number. Compare to the example in the notes. Models for the density of charge carriers due to the diffusion-drift equillibrium.

Models for the density of charge carriers due to the diffusion-drift equillibrium. Depletion zone - all the available electrons wander over to the p-zone, and all the available holes in p-zone are filled. Preview of the final results: The equations will be integrated and we shall obtain a relation for the total depletion zone d, d=dp+dn.