Improved theoretical minimum of the specific on-resistance of a superjunction
K. Akshay, Shreepad Karmalkar
Abstract
Abstract We derive simple closed-form solutions for the optimum pillar parameters—length L opt , width 2 W opt and doping N opt of a superjunction. The parameters yield the minimum specific on-resistance, R ONSP , for a target breakdown voltage, V BR,target , thereby solving a long standing design problem. The minimum R ONSP occurs for zero charge imbalance. Our estimates of N opt are higher and hence the R ONSP lower than in prior works by >30%. We show that, N opt depends on W opt alone, since for this doping, the p and n pillars are just fully depleted when the reverse bias equals the V BR of the one-dimensional p + n junction. Further, our derivation reveals that L opt depends on V BR,target alone since the field distribution associated with V BR,target is approximately uniform over L opt . In contrast, prior design solutions require numerical or iterative calculations, and are either physically opaque or give a distorted insight that L opt depends on W opt and N opt on L opt . Moreover, our solutions have a generic form that permits quick calculations across different materials. They are validated by technology computer-aided design simulation for low and wide band gap materials—Si and 4H-SiC. Their results for GaN and diamond are given to reveal the wide 100 V–30 kV application range of devices in these materials. The solutions are also used to reveal the scope for reducing the R ONSP of several fabricated devices reported in literature by process improvement.