PN junction's behavior near corners

[Assaf Peled]

Hey all,

Consider a general 2D configuration of a P+N junction where a small P+ material rectangle is placed upon a much larger N-material rectangle. So, the interface between the P+ and the N comprises a flat boundary line terminated on each side by a right-angled corner (hope I'm being clear enough). My question is how to find the depletion region's profile on the N side (shape and width) near these corners.

The depletion region along the flat boundary interface follows the simple 1D Poisson's eq. analysis, which is no longer valid when approaching the corner area.

Any idea on how to formulate an analytic expression for the depletion region around corners?

Thanks a Bunch

 

[marcusl]

The depletion zone is where the diffusion potential is balanced by the electrostatic potential, so you need to calculate both a potential and a streamline (for the diffusion current). You may be able to compute them both using conformal mapping-- in particular, the Schwartz-Christoffel transform. This will involve elliptic integrals so you need to decide how important it is to have an analytic va. numeric answer.