A Self-Consistent Two-Carrier Drift-Diffusion Framework for p-n Junctions: Extended Diode Equation, Power Dissipation, and Base Transit Time

Abstract

The classical theory of p-n junctions derives the current-voltage characteristic from minority-carrier diffusion alone: majority carriers are treated as an inert background, the quasi-neutral base as field-free, and the junction voltage as equal to the applied bias. These premises fail together under high bias and high-level injection, where the observed current roll-off is reproduced only by appending an empirical series resistance outside the junction physics. Here we develop a self-consistent two-carrier drift-diffusion framework that introduces no assumption beyond the classical ones. Excess majority carriers are shown to be electrostatically forced transport participants: the ambipolar diffusion equation, closed by exact two-sided boundary conditions, yields a unified excess-carrier profile. The resulting base field separates into an ohmic and a Dember component, and all four current components follow in closed form, their sum being position independent. At device level the framework closes into an extended diode equation that contains the Shockley equation as its low-injection, long-base limit and reproduces the n=2 roll-off intrinsically. The junction voltage emerges as a self-limiting drop confined to the space-charge region and separated from the applied bias by exact base drops. Two device-level corrections are quantified: at high current, 75-90% of the dissipation migrates from the junction into the quasi-neutral base, and field-assisted acceleration shortens the base transit time by up to a factor of six. Three parameter-free predictions follow: a universal ideality-factor crossover that passes through 3/2 when the boundary excess equals the doping, a high-injection onset voltage that scales as 119 mV per decade of doping, and a geometry factor that survives into high injection.