Revisiting the 1-D Theoretical Limit of Wide Bandgap Semiconductor Power Devices via Variational Calculus

Abstract

In wide-bandgap semiconductors with strongly nonlinear impact ionization coefficients, classical monotonic doping profiles may limit the reduction of specific on-resistance ( ${R}_{\text {on},\text {sp}}$ ) under avalanche-breakdown constraints. A variational formulation shows that a non-monotonic, U-shaped profile can emerge as a candidate solution. DE optimization and TCAD simulations further support its performance advantage: a steep surface electric-field gradient spatially confines avalanche generation. Consequently, the U-shaped profile achieves a lower ${R}_{\text {on},\text {sp}}$ than uniform and conventional monotonic profiles while meeting the required voltage-blocking capability, providing guidance for doping-profile optimization in advanced power devices.