Ideal RESURF Geometries

In order to maximize the OFF-state breakdown voltage (BV) of semiconductor devices, the slope of the electric field in the drift extension along the current flow direction ( $ E_{x}$ field) should be zero. This is achieved using the reduced surface field (RESURF) effect. This paper demonstrates a method to construct devices that obey Poisson’s equation and satisfy the ideal RESURF condition giving zero slope in $ E_{x}$ throughout the 2-D device region. The designs are obtained by shaping the device geometry and the boundaries and by applying the proper potentials at the boundaries. Using this method, ideal designs of the drift extension have been derived for devices based on graded doping, graded thickness, and graded field-plate potential. In addition, 2-D solutions have been derived for periodic superjunction device geometries. A solution for devices that combine several types of field shaping is demonstrated. Finally, the effect of nonideal geometries on the BV in more realistic geometries is discussed.