Depletion width

Formation in a MOS capacitor

where ${\displaystyle w_{P}}$ and ${\displaystyle w_{N}}$ are depletion widths in the p and n semiconductor, respectively. This condition ensures that the net negative acceptor charge exactly balances the net positive donor charge. The total depletion width in this case is the sum ${\displaystyle w=w_{N}+w_{P}}$. A full derivation for the depletion width is presented in reference. This derivation is based on solving the Poisson equation in one dimension – the dimension normal to the metallurgical junction. The electric field is zero outside of the depletion width (seen in above figure) and therefore Gauss's law implies that the charge density in each region balance – as shown by the first equation in this sub-section. Treating each region separately and substituting the charge density for each region into the Poisson equation eventually leads to a result for the depletion width. This result for the depletion width is: