Enhanced Theoretical Lower Limit for the Specific On-Resistance of a Silicon Balanced Superjunction

We propose a simple yet highly effective analytical model for the electric field distribution along the critical path in a balanced superjunction (SJ) power device. Using this electric field model for silicon SJ devices, we relate the breakdown voltage ( <tex-math notation="LaTeX">VBr</tex-math> ) to the pillar parameters, namely width ( <tex-math notation="LaTeX">2W</tex-math> ), length ( L ), and doping ( N ). Furthermore, we derive simple closed-form expressions for the optimum design parameters, <tex-math notation="LaTeX">Lₒₚₜ</tex-math> and <tex-math notation="LaTeX">Nₒₚₜ</tex-math> , which minimize the specific ON-resistance ( <tex-math notation="LaTeX">R_ON,sp</tex-math> ) for a target <tex-math notation="LaTeX">VBr</tex-math> and a given W . Analytical formulas for the optimum <tex-math notation="LaTeX">R_ON,sp</tex-math> and critical electric field are also provided. We show that our predictions of optimum <tex-math notation="LaTeX">R_ON,sp</tex-math> are lower than the lowest predictions made till date. Moreover, our model achieves the ideal relations of SJ, i.e., <tex-math notation="LaTeX">Lₒₚₜ∝ VBr</tex-math> , and <tex-math notation="LaTeX">Nₒₚₜ</tex-math> independent of <tex-math notation="LaTeX">VBr</tex-math> , leading to <tex-math notation="LaTeX">R_ON,sp</tex-math> <tex-math notation="LaTeX">∝</tex-math> <tex-math notation="LaTeX">VBr</tex-math> , except at high <tex-math notation="LaTeX">VBr</tex-math> in low W devices. Our theory unveils a crucial insight that the total charge ( <tex-math notation="LaTeX">qNₒₚₜ 2WLₒₚₜ</tex-math> ) of an optimum device remains constant for a target <tex-math notation="LaTeX">VBr</tex-math> , regardless of <tex-math notation="LaTeX">W</tex-math> . Our results greatly simplify the design process, avoiding the need of using iterative solvers. We validate our model using 2-D numerical simulations.