A Unified Optimization Model for Vertical Power High- k Superjunction With NPT and PT Modes

Abstract

This letter introduces a simplified electric field model for high- $\boldsymbol {k}$ superjunctions (H $\boldsymbol {k}$ SJs) under the punch-through (PT) mode, and its novel modification for the non-punch-through (NPT) mode, which is further extended to incorporate interface charges ( ${Q}_{\text {it}}$ ) at the heterointerface. A unified optimization framework for PT and NPT modes is developed and compares width-based and aspect ratio (AR)-based strategies, obtaining the minimum specific ON-resistance ( ${R}_{\text {on,sp}}$ ) under the designed breakdown voltage (BV). The analytical results of ${R}_{\text {on,sp}}$ are in good agreement with MEDICI simulations and a refined ${R}_{\text {on,sp}} \propto \text { BV}^{\text {1.37}}$ is obtained under given Hk-pillar width (b) and permittivity ratio ( ${K}_{\text {r}}$ ). It aslo reveals that H $\boldsymbol {k}$ SJs with the same product of b and ${K}_{\text {r}}$ exhibit identicalon-resistance. Furthermore, a theoretical limit of ${R}_{\text {on,sp}} \propto \text { BV}^{\text {1.06}}$ and an estimated saturation threshold for dielectric benefits are identified to reduce the need for high- $\boldsymbol {k}$ materials. This work establishes a compact and generalizable framework for modeling and optimizing HkSJs, supported by simulation benchmarks and offering practical guidance for device design.