Unified Physical Understanding of Current-Filament Stability in IGBTs Based on a 1-D Space-Charge-Region Framework

Abstract

We analyze the space-charge-region (SCR) physics governing current-filament stability in IGBTs using a one-dimensional model based on Gauss’s law and carrier continuity equations. We show that both clamped inductive switching (CIS) and unclamped inductive switching (UIS), despite traditionally being analyzed separately, are governed by the same SCR differential equations with different boundary conditions. This establishes a unified physical framework that explains the vertical electric-field formation in IGBT switching transients. Using this unified SCR model, we analyze the electrical conditions governing current-filament persistence and extinction. The critical current density $j_{\mathrm {crit}}$ , derived from the SCR voltage–current characteristics, is introduced as an isothermal electrical criterion under prescribed temperature and boundary conditions. In particular, a positive finite $j_{\mathrm {crit}}$ exists for high collector injection efficiency, whereas in SSCM no positive finite $j_{\mathrm {crit}}$ appears. This distinction indicates a stronger local tendency toward filament persistence in SSCM as the collector current approaches zero. These results establish a physics-based electrical criterion for filament stability and clarify the key factors governing IGBT robustness during high-current transient operation.