Analytical solution for two-dimensional current injection from shallow p-n junctions

An accurate analytical solution for the two-dimensional minority-carrier current spreading from a forward-biased p-n junction is presented. The structure considered is a very shallow junction on the top of a (infinitely large) substrate of thickness
W
. The back contact is characterized by a surface recombination velocity
S
. The solution of the boundary-value problem yields the ratio of the two-dimensional current
I_{2D}
to the one-dimensional current
I_{1D}
as a function of geometry, of
S
, and of the minority-carrier diffusion length and mobility. Device implications of the results are discussed.