Diode — the exponential gate

The diode's current grows exponentially with voltage; sealed exactly: e^(x+ln2) = 2e^x — current DOUBLES for every ln2·nVT of forward voltage, ≈ 17.9 mV at room temperature (sealed: floor(10⁴·ln2·0.02585) = 179): https://narrowhighway.com/s/1ee0d3ed486453eee0967146a531984888709198b39fb16a7b2c2a5f58ef1b73 . That knife-edge nonlinearity is why a diode can rectify — turn a symmetric radio wave into a one-way signal. The honest boundary: the famous '0.7 V drop' is a silicon rule of thumb (germanium ~0.3 V, LEDs 2–3 V) — material constants are measured, and deriving them needs semiconductor band physics, not a one-line formula.