A number of years ago I required a low voltage, extremely low current, voltage regulator. Normal Zener diodes do not function well at low currents. I became aware that the forward voltage of red LED's was approximately 1 Volt at even extremely low currents (less than 1 microamp). My question is (and I have been unable to find an answer), what physical properties determine the forward voltage of LED's at low currents? Manufacturer's data sheets all indicate that it is approximately 1 Volt at very low (zero?) current.