A unified analytical design reformulation for static performance optimization in Si, WBG, and UWBG devices

This paper presents a unified analytical reformulation and extension of existing drift-region design methods for high-voltage unipolar semiconductor devices. It enables unified design and performance optimization across a wide range of semiconductor materials like silicon (Si), wide-bandgap, and ultra-wide-bandgap semiconductors. The model provides closed-form expressions for the key performance parameters such as breakdown voltage (BV), critical electric field (Ecr), and depletion width (WD) using only doping concentration (ND) and intrinsic material properties. By assuming effective impact ionization coefficients via a geometric mean, the impact ionization integral can be solved analytically and then fitted using dimensionless parameters, eliminating the need for material-specific fitting. It applies to both non-punch-through and punch-through (PT) structures and guides designers in identifying optimal doping-thickness combinations. Applied to PT devices, the theoretical limits of the model predict 10%–15% improvement in conduction performance for all semiconductors across the practical BV range.