Shockley's ideal diode equation, I = Is (eV/VT − 1),
with the saturation current set by the semiconductor's bandgap. Note how little the
curve's shape changes between materials — and how much the knee voltage moves.
What is idealised here. The ideality factor is exactly 1, so no
recombination current; there is no series resistance, so the forward current
keeps rising exponentially instead of straightening into a line; and there is
no breakdown, so the reverse current stays at −Is
however negative V becomes. The saturation currents come from
Is ∝ e−Eg/kT with one
common prefactor, which is why they span twelve orders of magnitude across
these four materials. That value is only a starting point: type your own
Is into the field to match a datasheet or a measured
diode. Picking a material or changing the temperature puts the physical value
back.