please help me about nonliner transfer led function

i'm researching about nonliner of led in optical modutation. but i don't know what is nonliner transfer led function. i will appreciate if you can provide this function to me. Thank a lot.

I wanted to create a model of diodes for my simulator. I needed to find out what was the V/I curve for diodes.

So I measured real diodes, testing them at various current-versus-volt levels. I measured led's as well.

I plotted the data. The diode curve appears to be an exponential equation. Resembling 'Volts to some power equals amperes'. (It also needs a coefficient or two somewhere.)

I tried to fit different equations to the curve. For plain red led's, the best I could come up with is:

AMPS = (VOLTS * .51) ^ 29

This formula is only a crude approximation. It cannot be compared to the Shockley equation (scroll 45% down the website):

https://en.wikipedia.org/wiki/Shockley's_diode_equation

However I could never find out what values to insert in the Shockley equation, in order for me to be able to use it.

My simple formula cannot be applied to all colors of led's, nor all efficiencies, brightness levels, etc. The coefficients must be adjusted up or down, accordingly.

oh, i want't function which i can draw fuction:

if you know, please provide it to me. thank you very much

If you plot the equation and make n = 4, then the plot looks very much like that of a LED.

thank you, but i need the function that have a factor nonliner (ex factor nonliner =k).

The Shockley diode equation is for ideal diodes and holds the n factor( emission coefficient), the thermal Voltage VT=kT/q holds the k constant (Boltzmann)

All these things are on the wiki page and every good schoolbook: https://en.wikipedia.org/wiki/Diode
If this is not wath you need you have to spend some more time and words to you posts ;-) because otherwise it keeps guessing.

The I/V graphs as shown are non linear.
Vf of a diode changes with temperature. A 1n4007 has a Vf of 0.65V at room temp but this changes to around 1V at 1A and it also changes with temperature