An analytical model for punch-through limited breakdown voltage of planar junction with multiple floating field limiting rings

An appropriate model for punch-through (PT) limited breakdown voltage of a planar junction is presented for the first time as a function of the normalized epitaxial layer thickness and the critical depletion width of the cylindrical junction at breakdown in non-PT case. The results are applied to the planar junction structure with a single ring, taking into account three different breakdown modes. The problem of the multiple ring structure is solved using the equivalent ring method, which allows determination of the PT limited breakdown voltage and optimized ring spacings for the structure. Comparisons with two-dimensional device simulations using MEDICI show a good agreement.