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Here is an 'exact' solution for the carrier concentrations in the upper graph, and the band edge energies in the lower graph, as a function of position. The n-material is on the left and the p- on the right. There is a region near the center of the junction where the carrier concentrations, both n and p are small. This is the carrier depletion region where the charge density is dominated by the positive donor ions or the negative acceptors.
Clicking on the approximate choice for the solutions gives a frequently used approximate result based on the assumption that the carrier concentrations change abruptly from their bulk values to zero at the outer edges of the depletion zones. Turn off the autoscaling and watch each of the graphs as you switch between the two solutions to get some feeling for the success of the approximate scheme: both for the densities, and for the energies.
Why is the depletion layer thinner on the n-side than on the p-side?