• $summary_{type}$: application
• $word_{count}$: 170

Forward bias (positive to p, negative to n) reduces the barrier: $V_{eff}$ = $V_0$ - $V_{ext}$. Depletion narrows, majority carriers cross the junction, current rises exponentially: I = $I_0$(e^$\frac{eV}{nkT}$ - 1). The threshold voltage (~0.7 V Si, ~0.3 V Ge) is where significant current begins. Dynamic resistance $r_d$ = $\frac{nkT}{eI}$ — very low at operating point. Reverse bias (positive to n, negative to p) increases the barrier: $V_{eff}$ = $V_0$ + $V_{ext}$. Depletion widens, only minority carriers (thermally generated) contribute a tiny saturation current $I_0$ (~nA for Si). Current is nearly voltage-independent until breakdown. Zener breakdown occurs in thin junctions (heavy doping): strong field ionizes covalent bonds. Avalanche breakdown occurs in thick junctions: accelerated carriers cause impact ionization cascade. The diode equation I = $I_0$(e^$\frac{eV}{nkT}$ - 1) describes both regions: positive V gives exponential forward current, negative V gives -$I_0$ (saturation). At room temperature, eV/kT ≈ V/0.026.