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Forward Current versus Forward Voltage for Light Emitting Diodes

Anyone who has worked with light emitting diodes has noticed that there's a relationship between color and the forward voltage drop for the same current.

Intuitively, this makes sense, because higher frequency (shorter wavelength) light has higher energy than lower frequency light.

The relationship between  the frequency of a photon and its energy is given by the  Planck–Einstein equation:

E is energy
h is Planck's constant
v is the frequency

Numerically, Planck's constant is 4.136 x 10-15 eVs (electron-volts seconds)

The image below, from http://en.wikipedia.org/wiki/Electromagnetic_spectrum shows the wavelength and frequency of the visible spectrum as well as  the neighboring infrared and ultraviolet.

If we say red light corresponds to 675 nm (4.44x1014 Hz), we can compute the associated frequency as  photon energy as 1.8 eV. If we pick blue as 450 nm, the associated photon energy is 2.76 eV. Near infrared at say 900 nm has a photon energy of 1.38 eV.

Thus, we expect the range of expected forward voltage for an LED to range between 1.4V or so for an IR diode and 2.8V for white, based purely upon the physics of the emitted light.

 

The plot below shows the measured forward current as a function of forward  voltage for infrared, red, yellow, green and white LEDs. In general, the observed forward voltage corresponds to the values estimated from the Planck-Einstein equation. Agreement is not perfect because I don't know the exact frequency of the light emitted by each diode and because there is also a bulk resistance effect which increases the forward voltage for a given current, particularly at higher current levels.