Light emitting diodes and Planck's Constant

[Doom of Doom]

In my lab class we performed an experiment, in which we 'determined' the value of Planck's constant (value of h/e actually) by measuring the turn-on voltage for light emitting diodes of various colors. The idea is:

Given a light emitting diode that emits light with a maximum wavelength of \lambda (lowest energy light), determine that diodes 'turn-on' voltage (that is, the minimum amount of forward-biased voltage across the diode required to make it emit light). Then the relation \frac{hc}{\lambda}=e V_D holds, where h is Planck's constant and V_D is the minimum turn-on voltage.

I was quite surprised at how accurate our determination of h/e was. We got 4.2\pm.1 \times 10^{-15}Vs (compare to actual value of 4.135\times 10^{-15}).

I guess the 'turn-on' voltage should theoretically be equal to the difference in potential between the conduction bands of the n-type and p-type sides of the junction. But even with a small amount of voltage less that V_D, current still flows (albeit only a small amount) due to thermal fluctuations, since the Fermi levels of the two sides aren't equal anymore. But current really only starts to get going once you pass the threshold V_D voltage, which is when we first start to see emitted light. If we had a sensitive enough detector, we would be able to detect photons when holes and electrons recombine before this threshold voltage is passed, no? And these photons would have less energy than those with energy of eV_D.

Essentially, this experiment depends on the fact that we can't see any light coming from the diode until this Vd is passed. Is this a correct interpretation?

http://tinypic.com/r/2912qgx/7"
http://tinypic.com/r/2912qgx/7

 

[Doom of Doom]

This image is a good reference.