Bipolar Junction Transistor

In the active region the base-emitter junction is forward-biased (injection into the base), while the base-collector junction is reverse-biased (an attracting field toward the collector). In saturation both junctions are forward-biased, so V_CE drops to a minimum and I_C no longer scales proportionally with base current.

α is the common-base current coefficient (I_C/I_E ≤ 1, typically very close to 1), while β is the common-emitter coefficient (I_C/I_B). Since I_E=I_C+I_B, the two are algebraically linked directly — a small change in α near 1 produces a large change in β.

I_S decreases exponentially as the band gap increases. Germanium's narrower gap (≈0.66 eV vs silicon's ≈1.12 eV) gives a much larger I_S, so reaching the same collector current requires a much smaller V_BE — visible directly from $V_{BE}=V_T\ln(I_C/I_S)$.

The Early effect (base-width modulation) explains why the I_C(V_CE) output curves are not perfectly flat in the active region but slope slightly upward — the backward extrapolation of all curves meets the horizontal axis at a common point, $V_{CE}=-V_A$.