Fringing field of high-voltage planar p-i-n diodes with a nonuniformly doped guard ring

Abstract

An exact analytical solution to the problem of the electric-field distribution in a plane capacitor with infinitely long interelectrode space, thin electrodes, and a nonuniform surface charge at the boundary of an insulator that fills the capacitor was derived. Such a capacitor represents an adequate model of a p-i-n diode with shallow planar junctions, a stopper ring, and a lightly doped guard ring. It is shown that a guard ring with the surface charge density Q s varying over the semiconductor-free space interface makes it basically possible to reduce the largest value of the fringing field to the bulk value E0. To this end, it is necessary that (i) the width of the guard ring is at least three times as large as the depletion region thickness d and (ii) the quantity Q s is equal to-E0ɛ0(ɛ+1/2) in the internal region of the guard ring and increases gradually to E0ɛ0(ɛ+3/2) (if there is a stopper ring) or to zero (if there is no stopper ring) in a band that has a width no less than d and is located at the outer boundary of the guard ring. The results of calculations can be also used to optimize the doping profile in the diodes fabricated using silicon-on-insulator technology.