In this video, we will discuss Light Emitting Diode.

So, the Light Emitting Diode is basically a P-N junction.

The P-N junction made with materials that have

a very high radiative recombination probability.

So, here is a simple band diagram for a P-N junction.

So, at equilibrium, this carrier diffusion is

balanced by the electric field or the energy band bending built across the junction.

When you apply a forward bias as shown in this figure in the right,

then you lower the barrier,

the carrier diffusion takes place.

Now, if this is a long base diode,

then as the carriers diffuse,

the increased carrier concentration results in increased recombination rate,

so the carriers will recombine.

Now, if the material has

a low radiative transition probability, recombination probability,

then this recombination will probably be dominated by

non-radiative processes such as shockly whole read recombination or oj recombination.

But if your material has a very high radiative recombination probability,

then the recombination could be mainly

radiative and you get a lot of light coming out of your material,

and this is essentially the Light Emitting Diode.

So, the color or the spectrum of the light that you get

would be related to the energies of the recombining electrons and holes,

and if you look at the distribution of energy of the conduction band,

the electrons and the valence band holes,

there are basically congregated near the bottom of

the conduction band and the top of the valence band and

the lower energy site distribution

of the conduction band electron is basically determined by the density of states.

So, this goes up as square root of the energy and the high energy tail of

the energy distribution of

the conduction band electrons is determined mainly

by the Fermi-Dirac distribution function.

So, it decays exponentially with the energy on the high energy sites,

and same thing with the hole distribution.

So, the width of these electron energy distribution and

the hole energy distribution is basically of the order of the thermal energy, kT,

and therefore the width of

the energy distribution of the resulting photons of the light is also of the order of kT,

typically 2-3 kT and it has a sharp cutoff at the band gap energy.

If you plot the spectrum as a function of wavelength,

then of course the wavelength is inversely related to energy.

So, this a spectrum is flipped and you have a sharp cutoff due to band gap

at longer wavelengths side and you have

an exponential tail on the shorter wavelength side,

which is the high-energy site.

So, the width of the spectrum for a red LED as shown here centered

at 655 nanometer is about

24 nanometers and that's the again something of the order of kT,

thermal energy at room temperature.

If you plot the current versus the light intensity there basically linear because

one electron and one hole produces one photon.

So, they should be linearly proportional to each

other and if you plot I-V characteristic, I versus V,

then you get the standard exponential function

dictated by your diode equation, ideal diode equation.