Quick Design of a Superjunction Considering Charge Imbalance Due to Process Variations
K. Akshay, Shreepad Karmalkar
Abstract
The breakdown voltage, V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> , of a superjunction whose pillar parameters, namely doping, length, and width, are optimized to yield the least specific ON-resistance, R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> , for the specified V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">BR</sub> , falls drastically for even small charge imbalances. Hence, a structure fabricated with these target parameter values often has a VBR much lower than specified due to the charge imbalance caused by random process variations. We give an analytical solution for alternate target parameter values which yield the specified VBR in spite of process variations, with minimum sacrifice in R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ONSP</sub> . The solution is obtained by the method of Lagrange multipliers and a simple equation for the breakdown field versus charge imbalance. It is validated by T <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">CAD</sub> simulation. It can either be approximated to a closed-form or can yield the target parameter values accurately with just a few iterations. Apart from eliminating the tedious iterations of prior design methods, our solution provides two new insights: when compared with an optimum balanced device, a device optimized considering typical charge imbalance has significantly lower pillar doping but almost the same pillar length and width; the breakdown field of a balanced device is a power law function of the pillar length alone. Although illustrated for 4H-SiC structures with VBR,target of 1-10 kV, our solution should work for any semiconductor after material specific changes.